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Deck 12: The Conic Sections
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Question
Use the given information to find the equation of the hyperbola. The foci are 
and the directrices are 
A)
B)
C)
D)
E)
and the directrices are A)
B)
C)
D)
E)
Question
Determine the directrices for the ellipse and hyperbola. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the hyperbola. Specify the following: center, vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 
A)
center: 
; vertices: 
;
Foci:
;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;
Asymptotes:
.
B)
Center: 
;
Vertices:
;
Foci:
;
length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;
Asymptotes:
.
C)
center: 
; vertices: 
;
Foci:
;
Length of transverse axis: 4;
Length of conjugate axis: 4;
Eccentricity:
;
Asymptotes:
.
D)
center: 
; vertices: 
;
Foci:
;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;
Asymptotes:
.
E)
center: 
; vertices: 
;
Foci:
;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;
Asymptotes:
.
A)
center: ; vertices: ;Foci:
;Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
.B)
Center: ;Vertices:
;Foci:
; length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
.C)
center: ; vertices: ;Foci:
;Length of transverse axis: 4;
Length of conjugate axis: 4;
Eccentricity:
;Asymptotes:
.D)
center: ; vertices: ;Foci:
;Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
.E)
center: ; vertices: ;Foci:
;Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
. Question
Graph the ellipse. Specify the lengths of the major and minor axes, the foci, the center and the eccentricity. 
A) center: (- 2, 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;
Eccentricity:
B) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci:
;
Eccentricity:
C) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;
Eccentricity:
D) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci:
;
Eccentricity:
E) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;
Eccentricity:
A) center: (- 2, 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;Eccentricity:
B) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci:
;Eccentricity:
C) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;Eccentricity:
D) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci:
;Eccentricity:
E) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;Eccentricity:
Question
Graph the parabola. Specify the focus, directrix, vertex and focal width. 
A)
Focal width: 1
B)
Focal width: 5
C)
Focal width: 5
D)
Focal width: 5
E)
Focal width: 1
A)
Focal width: 1B)
Focal width: 5C)
Focal width: 5D)
Focal width: 5E)
Focal width: 1 Question
Find the equation of the tangent to the parabola at the given point. 
A) y = 2x - 16
B) y = 3x - 9
C) y = 2x - 9
D) y = 3x - 8
E) y = 2x - 8
A) y = 2x - 16
B) y = 3x - 9
C) y = 2x - 9
D) y = 3x - 8
E) y = 2x - 8
Question
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 
A)
vertices: 
;
Foci:
;
Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.
B)
vertices: 
;
Foci:
;
Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity:
;
Asymptotes:
.
C)
vertices: 
;
Foci:
;
Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity:
;
Asymptotes:
.
D)
vertices: 
;
Foci:
;
Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.
E)
vertices: 
;
Foci:
;
Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity:
;
Asymptotes:
.
A)
vertices: ;Foci:
;Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.B)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity:
;Asymptotes:
.C)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity:
;Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.E)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity:
;Asymptotes:
. Question
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 
A)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
B)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
C)
vertices:
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
D)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
E)
vertices: 
;
Foci:
;
length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
A)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.B)
vertices: ;Foci:
; Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.C)
vertices:
;Foci:
;Length of transverse axis:
; Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.E)
vertices: ;Foci:
; length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
. Question
Select the answer that represents the hyperbola as well as its eccentricity, center and values of 
, 
and 
. 
A)
Eccentricity: 
Center: 
B)
Eccentricity: 
Center: 
C)
Eccentricity: 
Center: 
D)
Eccentricity: 
Center: 
E)
Eccentricity: 
Center: 
, and . A)
Eccentricity: Center: B)
Eccentricity: Center: C)
Eccentricity: Center: D)
Eccentricity: Center: E)
Eccentricity: Center: Question
You are given an ellipse and a point P on the ellipse. Find 
and 
, the lengths of the focal radii. 
A)
B)
C)
D)
E)
and , the lengths of the focal radii. A)
B)
C)
D)
E)
Question
Graph the hyperbola. Specify the following: center, vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Suppose the line 
intersects the circle 
at points 
and 
. Find the length of the chord 
.
A)
B)
C)
D)
E)
intersects the circle at points and . Find the length of the chord .A)
B)
C)
D)
E)
Question
The point 
is the midpoint of a chord of the circle 
. Find the length of the chord.
A)
B)
C)
D)
E)
is the midpoint of a chord of the circle . Find the length of the chord.A)
B)
C)
D)
E)
Question
Graph the ellipse. Specify the lengths of the major and minor axes, the foci and the eccentricity. 
A) length of major axis: 8;
Length of minor axis: 6;
Foci:
;
Eccentricity:
B) length of major axis: 4;
Length of minor axis: 3;
Foci:
;
Eccentricity:
C) length of major axis: 9.6;
Length of minor axis: 7.2;
Foci:
;
Eccentricity:
D) length of major axis: 8;
Length of minor axis: 6;
Foci:
;
Eccentricity:
E) length of major axis: 4;
Length of minor axis: 3;
Foci:
;
Eccentricity:
A) length of major axis: 8;
Length of minor axis: 6;
Foci:
;Eccentricity:
B) length of major axis: 4;
Length of minor axis: 3;
Foci:
;Eccentricity:
C) length of major axis: 9.6;
Length of minor axis: 7.2;
Foci:
;Eccentricity:
D) length of major axis: 8;
Length of minor axis: 6;
Foci:
;Eccentricity:
E) length of major axis: 4;
Length of minor axis: 3;
Foci:
;Eccentricity:
Question
Find the equation of the tangent to the parabola at the given point. 
A) y = 5x + 8
B) y = 6x + 8
C) y = 6x + 9
D) y = 6x + 18
E) y = 5x + 9
A) y = 5x + 8
B) y = 6x + 8
C) y = 6x + 9
D) y = 6x + 18
E) y = 5x + 9
Question
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 
A)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
B)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
C)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
D)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
E)
vertices: 
;
Foci:
;
Length of transverse axis:
;
Length of conjugate axis:
;
Eccentricity:
;
Asymptotes:
.
A)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.B)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.C)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.E)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
. Question
Find the center and the radius of the circle that passes through the points 
A)
B) The center is at
and the radius is 
C) The center is at
and the radius is 
D) The center is at
and the radius is 7.
E) The center is at
and the radius is 
A)
B) The center is at
and the radius is C) The center is at
and the radius is D) The center is at
and the radius is 7.E) The center is at
and the radius is Question
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes. 
A)
vertices: 
;
Foci:
;
Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.
B)
vertices: 
;
Foci:
;
Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity:
;
Asymptotes:
.
C)
vertices:
;
Foci:
;
Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.
D)
vertices:
;
Foci:
;
Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity:
;
Asymptotes:
.
E)
vertices: 
;
Foci:
;
Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity:
Asymptotes: 
.
A)
vertices: ;Foci:
;Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.B)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity:
;Asymptotes:
.C)
vertices: ;Foci:
;Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity:
;Asymptotes:
.E)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity:
Asymptotes: . Question
Use the given information to find the equation of the ellipse. The foci are 
and the directrices are 
.
A)
B)
C)
D)
E)
and the directrices are .A)
B)
C)
D)
E)
Question
Graph the ellipse. Specify the lengths of the major and minor axes, the foci, the center and the eccentricity. 
A) center: (0, 5);
Degenerate ellipse
B) center: (1,
);
Degenerate ellipse
C) center: (5,0);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;
Eccentricity:
D) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;
Eccentricity:
E) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;
Eccentricity:
A) center: (0, 5);
Degenerate ellipse
B) center: (1,
);Degenerate ellipse
C) center: (5,0);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;Eccentricity:
D) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;Eccentricity:
E) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;Eccentricity:
Question
An angle of rotation is specified, followed by the coordinates of a point in the 
system. Find the coordinates of the point with respect to the 
system. 
A)
B)
C)
D)
E)
system. Find the coordinates of the point with respect to the system. A)
B)
C)
D)
E)
Question
Select the graph that represents the given conic section. If the conic is a parabola, specify (using rectangular coordinates) the vertex and directrix. If the conic is an ellipse, specify the center, the eccentricity, and the lengths of the major and minor axes. If the conic is a hyperbola, specify the center, the eccentricity, and the lengths of the transverse and conjugate axes. 
A)
Vertex: 
Directrix: 
B)
Vertex: 
Directrix: 
C)
Center: 
Eccentricity: 
Major axis length: 
Minor axis length:
D)
Vertex: 
Directrix: 
E)
Vertex: 
Directrix: 
A)
Vertex: Directrix: B)
Vertex: Directrix: C)
Center: Eccentricity: Major axis length: Minor axis length:
D)
Vertex: Directrix: E)
Vertex: Directrix: Question
Find 
and 
, where 
is the (acute) angle of rotation that eliminates the 
-term. Note: You are not asked to graph the equation. 
A)
B)
C)
D)
E)
and , where is the (acute) angle of rotation that eliminates the -term. Note: You are not asked to graph the equation. A)
B)
C)
D)
E)
Question
Find 
and 
, where 
is the (acute) angle of rotation that eliminates the 
-term. Note: You are not asked to graph the equation. 
A)
B)
C)
D)
E)
and , where is the (acute) angle of rotation that eliminates the -term. Note: You are not asked to graph the equation. A)
B)
C)
D)
E)
Question
Determine the graph that represents the equation. 
A)
B)
C)
D)
E) no graph
A)
B)
C)
D)
E) no graph
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Deck 12: The Conic Sections
1
Use the given information to find the equation of the hyperbola. The foci are and the directrices are
A)
B)
C)
D)
E)
and the directrices are A)
B)
C)
D)
E)
2
Determine the directrices for the ellipse and hyperbola.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Graph the hyperbola. Specify the following: center, vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes.
A) center: ; vertices: ;
Foci: ;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: ;
Asymptotes: .
B)
Center: ;
Vertices: ;
Foci: ;
length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: ;
Asymptotes: .
C) center: ; vertices: ;
Foci: ;
Length of transverse axis: 4;
Length of conjugate axis: 4;
Eccentricity: ;
Asymptotes: .
D) center: ; vertices: ;
Foci: ;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: ;
Asymptotes: .
E) center: ; vertices: ;
Foci: ;
Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity: ;
Asymptotes: .
A)
center: ; vertices: ;Foci:
;Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
.B)
Center: ;Vertices:
;Foci:
; length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
.C)
center: ; vertices: ;Foci:
;Length of transverse axis: 4;
Length of conjugate axis: 4;
Eccentricity:
;Asymptotes:
.D)
center: ; vertices: ;Foci:
;Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
.E)
center: ; vertices: ;Foci:
;Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
. center: ; vertices: ;Foci:
;Length of transverse axis: 8;
Length of conjugate axis: 8;
Eccentricity:
;Asymptotes:
. 4
Graph the ellipse. Specify the lengths of the major and minor axes, the foci, the center and the eccentricity.
A) center: (- 2, 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci: ;
Eccentricity:
B) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci: ;
Eccentricity:
C) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci: ;
Eccentricity:
D) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci: ;
Eccentricity:
E) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci: ;
Eccentricity:
A) center: (- 2, 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;Eccentricity:
B) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci:
;Eccentricity:
C) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;Eccentricity:
D) center: (1, - 2.5);
Length of major axis: 3;
Length of minor axis: 2;
Foci:
;Eccentricity:
E) center: (2, - 5);
Length of major axis: 6;
Length of minor axis: 4;
Foci:
;Eccentricity:
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5
Graph the parabola. Specify the focus, directrix, vertex and focal width.
A) Focal width: 1
B) Focal width: 5
C) Focal width: 5
D) Focal width: 5
E) Focal width: 1
A)
Focal width: 1B)
Focal width: 5C)
Focal width: 5D)
Focal width: 5E)
Focal width: 1 Unlock Deck
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6
Find the equation of the tangent to the parabola at the given point.
A) y = 2x - 16
B) y = 3x - 9
C) y = 2x - 9
D) y = 3x - 8
E) y = 2x - 8
A) y = 2x - 16
B) y = 3x - 9
C) y = 2x - 9
D) y = 3x - 8
E) y = 2x - 8
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7
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes.
A) vertices: ;
Foci: ;
Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes: .
B) vertices: ;
Foci: ;
Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity: ;
Asymptotes: .
C) vertices: ;
Foci: ;
Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity: ;
Asymptotes: .
D) vertices: ;
Foci: ;
Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes: .
E) vertices: ;
Foci: ;
Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity: ;
Asymptotes: .
A)
vertices: ;Foci:
;Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.B)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity:
;Asymptotes:
.C)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity:
;Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis: 10;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.E)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 10;
Eccentricity:
;Asymptotes:
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8
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes.
A) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
B) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
C)
vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
D) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
E) vertices: ;
Foci: ;
length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
A)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.B)
vertices: ;Foci:
; Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.C)
vertices:
;Foci:
;Length of transverse axis:
; Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.E)
vertices: ;Foci:
; length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
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9
Select the answer that represents the hyperbola as well as its eccentricity, center and values of , and .
A) Eccentricity: Center:
B) Eccentricity: Center:
C) Eccentricity: Center:
D) Eccentricity: Center:
E) Eccentricity: Center:
, and . A)
Eccentricity: Center: B)
Eccentricity: Center: C)
Eccentricity: Center: D)
Eccentricity: Center: E)
Eccentricity: Center: Unlock Deck
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10
You are given an ellipse and a point P on the ellipse. Find and , the lengths of the focal radii.
A)
B)
C)
D)
E)
and , the lengths of the focal radii. A)
B)
C)
D)
E)
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11
Graph the hyperbola. Specify the following: center, vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Suppose the line intersects the circle at points and . Find the length of the chord .
A)
B)
C)
D)
E)
intersects the circle at points and . Find the length of the chord .A)
B)
C)
D)
E)
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13
The point is the midpoint of a chord of the circle . Find the length of the chord.
A)
B)
C)
D)
E)
is the midpoint of a chord of the circle . Find the length of the chord.A)
B)
C)
D)
E)
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14
Graph the ellipse. Specify the lengths of the major and minor axes, the foci and the eccentricity.
A) length of major axis: 8;
Length of minor axis: 6;
Foci: ;
Eccentricity:
B) length of major axis: 4;
Length of minor axis: 3;
Foci: ;
Eccentricity:
C) length of major axis: 9.6;
Length of minor axis: 7.2;
Foci: ;
Eccentricity:
D) length of major axis: 8;
Length of minor axis: 6;
Foci: ;
Eccentricity:
E) length of major axis: 4;
Length of minor axis: 3;
Foci: ;
Eccentricity:
A) length of major axis: 8;
Length of minor axis: 6;
Foci:
;Eccentricity:
B) length of major axis: 4;
Length of minor axis: 3;
Foci:
;Eccentricity:
C) length of major axis: 9.6;
Length of minor axis: 7.2;
Foci:
;Eccentricity:
D) length of major axis: 8;
Length of minor axis: 6;
Foci:
;Eccentricity:
E) length of major axis: 4;
Length of minor axis: 3;
Foci:
;Eccentricity:
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15
Find the equation of the tangent to the parabola at the given point.
A) y = 5x + 8
B) y = 6x + 8
C) y = 6x + 9
D) y = 6x + 18
E) y = 5x + 9
A) y = 5x + 8
B) y = 6x + 8
C) y = 6x + 9
D) y = 6x + 18
E) y = 5x + 9
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16
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes.
A) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
B) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
C) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
D) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
E) vertices: ;
Foci: ;
Length of transverse axis: ;
Length of conjugate axis: ;
Eccentricity: ;
Asymptotes: .
A)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.B)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.C)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
.E)
vertices: ;Foci:
;Length of transverse axis:
;Length of conjugate axis:
;Eccentricity:
;Asymptotes:
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17
Find the center and the radius of the circle that passes through the points
A)
B) The center is at and the radius is
C) The center is at and the radius is
D) The center is at and the radius is 7.
E) The center is at and the radius is
A)
B) The center is at
and the radius is C) The center is at
and the radius is D) The center is at
and the radius is 7.E) The center is at
and the radius is Unlock Deck
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18
Graph the hyperbola. Specify the following: vertices, foci, lengths of transverse and conjugate axes, eccentricity, and equations of the asymptotes.
A) vertices: ;
Foci: ;
Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes: .
B) vertices: ;
Foci: ;
Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity: ;
Asymptotes: .
C) vertices: ;
Foci: ;
Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes: .
D) vertices: ;
Foci: ;
Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity: ;
Asymptotes: .
E) vertices: ;
Foci: ;
Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity: Asymptotes: .
A)
vertices: ;Foci:
;Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.B)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity:
;Asymptotes:
.C)
vertices: ;Foci:
;Length of transverse axis: 4;
Length of conjugate axis: 2;
Eccentricity:
Asymptotes:
.D)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 12;
Eccentricity:
;Asymptotes:
.E)
vertices: ;Foci:
;Length of transverse axis: 2;
Length of conjugate axis: 4;
Eccentricity:
Asymptotes: . Unlock Deck
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19
Use the given information to find the equation of the ellipse. The foci are and the directrices are .
A)
B)
C)
D)
E)
and the directrices are .A)
B)
C)
D)
E)
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20
Graph the ellipse. Specify the lengths of the major and minor axes, the foci, the center and the eccentricity.
A) center: (0, 5);
Degenerate ellipse
B) center: (1, );
Degenerate ellipse
C) center: (5,0);
Length of major axis: 10;
Length of minor axis: 4;
Foci: ;
Eccentricity:
D) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci: ;
Eccentricity:
E) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci: ;
Eccentricity:
A) center: (0, 5);
Degenerate ellipse
B) center: (1,
);Degenerate ellipse
C) center: (5,0);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;Eccentricity:
D) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;Eccentricity:
E) center: (0, 5);
Length of major axis: 10;
Length of minor axis: 4;
Foci:
;Eccentricity:
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21
An angle of rotation is specified, followed by the coordinates of a point in the system. Find the coordinates of the point with respect to the system.
A)
B)
C)
D)
E)
system. Find the coordinates of the point with respect to the system. A)
B)
C)
D)
E)
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22
Select the graph that represents the given conic section. If the conic is a parabola, specify (using rectangular coordinates) the vertex and directrix. If the conic is an ellipse, specify the center, the eccentricity, and the lengths of the major and minor axes. If the conic is a hyperbola, specify the center, the eccentricity, and the lengths of the transverse and conjugate axes.
A) Vertex: Directrix:
B) Vertex: Directrix:
C) Center: Eccentricity: Major axis length:
Minor axis length:
D) Vertex: Directrix:
E) Vertex: Directrix:
A)
Vertex: Directrix: B)
Vertex: Directrix: C)
Center: Eccentricity: Major axis length: Minor axis length:
D)
Vertex: Directrix: E)
Vertex: Directrix: Unlock Deck
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23
Find and , where is the (acute) angle of rotation that eliminates the -term. Note: You are not asked to graph the equation.
A)
B)
C)
D)
E)
and , where is the (acute) angle of rotation that eliminates the -term. Note: You are not asked to graph the equation. A)
B)
C)
D)
E)
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24
Find and , where is the (acute) angle of rotation that eliminates the -term. Note: You are not asked to graph the equation.
A)
B)
C)
D)
E)
and , where is the (acute) angle of rotation that eliminates the -term. Note: You are not asked to graph the equation. A)
B)
C)
D)
E)
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25
Determine the graph that represents the equation.
A)
B)
C)
D)
E) no graph
A)
B)
C)
D)
E) no graph
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Unlock Deck
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