Exam 6: Conic Sections

Solve the problem. -A reflecting telescope contains a parabolic mirror. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

(Multiple Choice)

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Question 41

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

(Multiple Choice)

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Question 42

Find an equation for the ellipse described. -Center at (0, 0); focus at (0, -5); vertex at (0, 8)

(Multiple Choice)

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Question 43

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $4 x ^ { 2 } - 16 y ^ { 2 } = 64$

(Multiple Choice)

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Question 44

Find an equation for the ellipse described. -Foci at (1, 4)and (-5, 4); vertex at (-8, 4)

(Multiple Choice)

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Question 45

Find the equation in standard form of the parabola described. -The vertex has coordinates (9, -3), and the focus has coordinates (9, -7).

(Multiple Choice)

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Question 46

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } - 8 x - 64 y - 64 = 0$

(Multiple Choice)

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Question 47

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y - 4 ) ^ { 2 } = 12 ( x + 2 )$

(Multiple Choice)

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Question 48

Find the equation in standard form of the parabola described. -The focus has coordinates (-15, 0), and the equation of the directrix is x = 15.

(Multiple Choice)

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Question 49

Convert the equation to the standard form for a hyperbola by completing the square. - $9 x ^ { 2 } - 4 y ^ { 2 } - 36 x - 8 y - 4 = 0$

(Multiple Choice)

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Question 50

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - ( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$

(Multiple Choice)

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Question 51

Graph the hyperbola. - $(x-2)^{2}-9(y-2)^{2}=9$ $Graph the hyperbola. - (x-2)^{2}-9(y-2)^{2}=9$

(Multiple Choice)

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Question 52

Graph the hyperbola. - $\frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$ $Graph the hyperbola. - \frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$

(Multiple Choice)

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Question 53

Find an equation for the ellipse described. -Center at (0, 0); focus at (-5, 0); vertex at (8, 0)

(Multiple Choice)

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Question 54

Graph the hyperbola. - $( y + 1 ) ^ { 2 } - ( x + 2 ) ^ { 2 } = 3$

(Multiple Choice)

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Question 55

Graph the equation. - $y^{2}=-16 x$ $Graph the equation. - y^{2}=-16 x$

(Multiple Choice)

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Question 56

Find an equation for the ellipse described. -Center (0, 0); major axis vertical with length 12; length of minor axis is 8

(Multiple Choice)

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Question 57

Find an equation for the ellipse described. -Focus at (0, -6); vertices at (0, -7)and (0, 7)

(Multiple Choice)

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Question 58

Graph the equation. - $9 ( x + 2 ) ^ { 2 } + 4 ( y + 1 ) ^ { 2 } = 36$ $Graph the equation. - 9 ( x + 2 ) ^ { 2 } + 4 ( y + 1 ) ^ { 2 } = 36$

(Multiple Choice)

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Question 59

Find the equation in standard form of the parabola described. -The vertex has coordinates (3, -5), and the focus has coordinates (4, -5).

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Question 60

Showing 41 - 60 of 97

Solve the problem. -A reflecting telescope contains a parabolic mirror. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Find an equation for the ellipse described. -Center at (0, 0); focus at (0, -5); vertex at (0, 8)

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $4 x ^ { 2 } - 16 y ^ { 2 } = 64$

Find an equation for the ellipse described. -Foci at (1, 4)and (-5, 4); vertex at (-8, 4)

Find the equation in standard form of the parabola described. -The vertex has coordinates (9, -3), and the focus has coordinates (9, -7).

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } - 8 x - 64 y - 64 = 0$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y - 4 ) ^ { 2 } = 12 ( x + 2 )$

Find the equation in standard form of the parabola described. -The focus has coordinates (-15, 0), and the equation of the directrix is x = 15.

Convert the equation to the standard form for a hyperbola by completing the square. - $9 x ^ { 2 } - 4 y ^ { 2 } - 36 x - 8 y - 4 = 0$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - ( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$

Graph the hyperbola. - $(x-2)^{2}-9(y-2)^{2}=9$ $Graph the hyperbola. - (x-2)^{2}-9(y-2)^{2}=9$

Graph the hyperbola. - $\frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$ $Graph the hyperbola. - \frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$

Find an equation for the ellipse described. -Center at (0, 0); focus at (-5, 0); vertex at (8, 0)

Graph the hyperbola. - $( y + 1 ) ^ { 2 } - ( x + 2 ) ^ { 2 } = 3$

Graph the equation. - $y^{2}=-16 x$ $Graph the equation. - y^{2}=-16 x$

Find an equation for the ellipse described. -Center (0, 0); major axis vertical with length 12; length of minor axis is 8

Find an equation for the ellipse described. -Focus at (0, -6); vertices at (0, -7)and (0, 7)

Graph the equation. - $9 ( x + 2 ) ^ { 2 } + 4 ( y + 1 ) ^ { 2 } = 36$ $Graph the equation. - 9 ( x + 2 ) ^ { 2 } + 4 ( y + 1 ) ^ { 2 } = 36$

Find the equation in standard form of the parabola described. -The vertex has coordinates (3, -5), and the focus has coordinates (4, -5).

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Exam 6: Conic Sections

Solve the problem. -A reflecting telescope contains a parabolic mirror. If the mirror is 24 inches across at its opening and is 4 feet deep, where will the light be concentrated?

Find the center, foci, and vertices of the ellipse. - x24+y216=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 14x2​+16y2​=1

Find an equation for the ellipse described. -Center at (0, 0); focus at (0, -5); vertex at (0, 8)

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - 4x2−16y2=644 x ^ { 2 } - 16 y ^ { 2 } = 644x2−16y2=64

Find an equation for the ellipse described. -Foci at (1, 4)and (-5, 4); vertex at (-8, 4)

Find the equation in standard form of the parabola described. -The vertex has coordinates (9, -3), and the focus has coordinates (9, -7).

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - x2−16y2−8x−64y−64=0x ^ { 2 } - 16 y ^ { 2 } - 8 x - 64 y - 64 = 0x2−16y2−8x−64y−64=0

Find the vertex, focus, and directrix of the parabola with the given equation. - (y−4)2=12(x+2)( y - 4 ) ^ { 2 } = 12 ( x + 2 )(y−4)2=12(x+2)

Find the equation in standard form of the parabola described. -The focus has coordinates (-15, 0), and the equation of the directrix is x = 15.

Convert the equation to the standard form for a hyperbola by completing the square. - 9x2−4y2−36x−8y−4=09 x ^ { 2 } - 4 y ^ { 2 } - 36 x - 8 y - 4 = 09x2−4y2−36x−8y−4=0

Find the vertex, focus, and directrix of the parabola. Graph the equation. - (y+1)2=−8(x+2)( y + 1 ) ^ { 2 } = - 8 ( x + 2 )(y+1)2=−8(x+2)

Graph the hyperbola. - (x−2)2−9(y−2)2=9(x-2)^{2}-9(y-2)^{2}=9(x−2)2−9(y−2)2=9

Graph the hyperbola. - (y+1)29−(x−2)216=1\frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 19(y+1)2​−16(x−2)2​=1

Find an equation for the ellipse described. -Center at (0, 0); focus at (-5, 0); vertex at (8, 0)

Graph the hyperbola. - (y+1)2−(x+2)2=3( y + 1 ) ^ { 2 } - ( x + 2 ) ^ { 2 } = 3(y+1)2−(x+2)2=3

Graph the equation. - y2=−16xy^{2}=-16 xy2=−16x

Find an equation for the ellipse described. -Center (0, 0); major axis vertical with length 12; length of minor axis is 8

Find an equation for the ellipse described. -Focus at (0, -6); vertices at (0, -7)and (0, 7)

Graph the equation. - 9(x+2)2+4(y+1)2=369 ( x + 2 ) ^ { 2 } + 4 ( y + 1 ) ^ { 2 } = 369(x+2)2+4(y+1)2=36

Find the equation in standard form of the parabola described. -The vertex has coordinates (3, -5), and the focus has coordinates (4, -5).

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $4 x ^ { 2 } - 16 y ^ { 2 } = 64$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } - 8 x - 64 y - 64 = 0$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y - 4 ) ^ { 2 } = 12 ( x + 2 )$

Convert the equation to the standard form for a hyperbola by completing the square. - $9 x ^ { 2 } - 4 y ^ { 2 } - 36 x - 8 y - 4 = 0$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - ( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$

Graph the hyperbola. - $(x-2)^{2}-9(y-2)^{2}=9$ $Graph the hyperbola. - (x-2)^{2}-9(y-2)^{2}=9$

Graph the hyperbola. - $\frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$ $Graph the hyperbola. - \frac { ( y + 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$

Graph the hyperbola. - $( y + 1 ) ^ { 2 } - ( x + 2 ) ^ { 2 } = 3$

Graph the equation. - $y^{2}=-16 x$ $Graph the equation. - y^{2}=-16 x$

Graph the equation. - $9 ( x + 2 ) ^ { 2 } + 4 ( y + 1 ) ^ { 2 } = 36$ $Graph the equation. - 9 ( x + 2 ) ^ { 2 } + 4 ( y + 1 ) ^ { 2 } = 36$