Question 1

Find an equation for the conic whose graph is shown.

Accepted Answer

A)  $x ^ { 2 } = 4 ( y + 3 )$ 
B)  $x ^ { 2 } = 3 ( y + 3 )$ 
C)  $y ^ { 2 } = 12 ( x + 3 )$ 
D)  $\frac { x } { 12 } = ( y + 3 ) ^ { 2 }$ 
E)  $x ^ { 2 } = 12 ( y + 3 )$ 
A)  $x ^ { 2 } = 4 ( y + 3 )$ 
B)  $x ^ { 2 } = 3 ( y + 3 )$ 
C)  $y ^ { 2 } = 12 ( x + 3 )$ 
D)  $\frac { x } { 12 } = ( y + 3 ) ^ { 2 }$ 
E)  $x ^ { 2 } = 12 ( y + 3 )$

Question 2

Sketch the graph of the ellipse. $$\frac { ( x - 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$$

Accepted Answer

The answer of Sketch the graph of the ellipse. \[\frac...

Question 3

Find an equation of the parabola whose graph is shown.

Accepted Answer

The answer of Find an equation of the parabola whose...

Question 4

Find an equation for the parabola with vertex $( 5,5 )$ 
and directrix $y - a x i s$ 
.

Accepted Answer

The answer of Find an equation for the parabola with...

Question 5

Find an equation for the parabola with vertex $( 5,5 )$ 
and directrix $y - \text { axis }$ 
.

Accepted Answer

The answer of Find an equation for the parabola with...

Question 6

Determine the $\overline { X Y }$ 
- coordinates of $( - 2,5 )$ 
if the axes are rotated through an angle $\phi = 30 ^ { \circ }$ 
.

Accepted Answer

The answer of Determine the $\overline { X Y }$...

Question 7

Find an equation for the conic whose graph is shown.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Question 8

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Accepted Answer

A) Vertices: $( 0 , \pm \sqrt { 2 } )$ , foci: $( 0 , \pm 2 )$ 
B) Vertices: $( \pm 2,0 )$, foci: $( 0 , \pm \sqrt { 2 } )$ 
C) Vertices: $( 0 , \pm 2 )$, foci: $( 0 , \pm \sqrt { 2 } )$ 
D) Vertices: $( 0 , \pm 2 )$, foci: $( \pm \sqrt { 2 } , 0 )$ 
E)  none of these 
A) Vertices: $( 0 , \pm \sqrt { 2 } )$ , foci: $( 0 , \pm 2 )$ 
B) Vertices: $( \pm 2,0 )$, foci: $( 0 , \pm \sqrt { 2 } )$ 
C) Vertices: $( 0 , \pm 2 )$, foci: $( 0 , \pm \sqrt { 2 } )$ 
D) Vertices: $( 0 , \pm 2 )$, foci: $( \pm \sqrt { 2 } , 0 )$ 
E)  none of these

Question 9

Write a polar equation of a hyperbola with eccentricity $3$ and directrix $r = 2 \csc \theta$

Accepted Answer

A)  $r= \frac { 3 } { 1 + 3 \cos \theta }$ 
B)  $r = \frac { 3 } { 1 - 3 \sin \theta }$ 
C)  $r = \frac { 2 } { 2 + 3 \cos }$ 
D)  $r = \frac { 6 } { 1 + 3 \sin \theta }$ 
E)  $r= \frac { 6 } { 1 - 3 \sin \theta }$ 
A)  $r= \frac { 3 } { 1 + 3 \cos \theta }$ 
B)  $r = \frac { 3 } { 1 - 3 \sin \theta }$ 
C)  $r = \frac { 2 } { 2 + 3 \cos }$ 
D)  $r = \frac { 6 } { 1 + 3 \sin \theta }$ 
E)  $r= \frac { 6 } { 1 - 3 \sin \theta }$

Question 10

Find the vertices of the hyperbola. $16 y ^ { 2 } - 4 x ^ { 2 } = 64$

Accepted Answer

A)  $( 2,0 )$ 
B)  $( 0 , \pm 1 )$ 
C)  $( \pm 2,0 )$ 
D)  $( 0 , \pm 2 )$ 
E)  none of these 
A)  $( 2,0 )$ 
B)  $( 0 , \pm 1 )$ 
C)  $( \pm 2,0 )$ 
D)  $( 0 , \pm 2 )$ 
E)  none of these

Question 11

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Accepted Answer

Vertices:

Question 12

Find the vertices of the hyperbola. $16 y ^ { 2 } - 4 x ^ { 2 } = 64$

Accepted Answer

The answer of Find the vertices of the hyperbola. \(16...

Question 13

Find an equation for the ellipse with center at the origin, major axis of length $2 \sqrt { 7 }$ 
, minor axis of length $2 \sqrt { 3 }$ 
, and whose foci lie on the $y$ 
-axis.

Accepted Answer

The answer of Find an equation for the ellipse with...

Question 14

Find the vertex, and directrix of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Accepted Answer

A)  $V ( 6 , - 1 ) , x = 0$ 
B)  $V ( 3 , - 1 )$ , $x = 0$ 
C)  $V ( 6 , - 1 ) , y = 0$ 
D)  $V ( 4 , - 1 ) , y = - 1$ 
E)  $V ( 6,0 ) , x = - 1$ 
A)  $V ( 6 , - 1 ) , x = 0$ 
B)  $V ( 3 , - 1 )$ , $x = 0$ 
C)  $V ( 6 , - 1 ) , y = 0$ 
D)  $V ( 4 , - 1 ) , y = - 1$ 
E)  $V ( 6,0 ) , x = - 1$

Question 15

Find an equation for the conic whose graph is shown.

Accepted Answer

The answer of Find an equation for the conic whose...

Question 16

Find an equation of the parabola whose graph is shown.

Accepted Answer

The answer of Find an equation of the parabola whose...

Question 17

Find an equation for the conic whose graph is shown.

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
E)  $9 y ^ { 2 } - \frac { x ^ { 2 } } { 16 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
E)  $9 y ^ { 2 } - \frac { x ^ { 2 } } { 16 } = 1$

Question 18

Find an equation for the conic whose graph is shown.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Question 19

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Accepted Answer

A)  $( x + 2 ) ^ { 2 } = 9 ( y - 3 )$
, parabola 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 81 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$
, ellipse 
C)  $\frac { ( x + 2 ) ^ { 2 } } { 8 } - \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1$
, hyperbola 
D)  $\frac { ( x + 3 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 3 } = 1$
, hyperbola 
E)  none of these 
A)  $( x + 2 ) ^ { 2 } = 9 ( y - 3 )$
, parabola 
B)  $\frac { ( x + 2 ) ^ { 2 } } { 81 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$
, ellipse 
C)  $\frac { ( x + 2 ) ^ { 2 } } { 8 } - \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1$
, hyperbola 
D)  $\frac { ( x + 3 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 3 } = 1$
, hyperbola 
E)  none of these

Question 20

A cannon fires a cannonball as shown in the figure. The path of the cannonball is a parabola with vertex at the highest point of the path. If the cannonball lands 1600 ft from the cannon and the highest point it reaches is 2400 ft above the ground, find an equation for the path of the cannonball. Place the origin at the location of the cannon.

Accepted Answer

A)  $( x - 1200 ) ^ { 2 } = - \frac { 400 } { 3 } ( y - 800 )$ 
B)  $( x - 800 ) ^ { 2 } = - \frac { 400 } { 3 } ( y - 2400 )$ 
C)  $( x - 800 ) ^ { 2 } = - \frac { 800 } { 3 } ( y - 2400 )$ 
D)  $( x - 2400 ) ^ { 2 } = - \frac { 800 } { 3 } ( y - 800 )$ 
E)  none of these 
A)  $( x - 1200 ) ^ { 2 } = - \frac { 400 } { 3 } ( y - 800 )$ 
B)  $( x - 800 ) ^ { 2 } = - \frac { 400 } { 3 } ( y - 2400 )$ 
C)  $( x - 800 ) ^ { 2 } = - \frac { 800 } { 3 } ( y - 2400 )$ 
D)  $( x - 2400 ) ^ { 2 } = - \frac { 800 } { 3 } ( y - 800 )$ 
E)  none of these

Find an equation for the conic whose graph is shown.

Sketch the graph of the ellipse. $\frac { ( x - 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$

Find an equation of the parabola whose graph is shown.

Find an equation for the parabola with vertex $( 5,5 )$ and directrix $y - a x i s$ .

Find an equation for the parabola with vertex $( 5,5 )$ and directrix $y - \text { axis }$ .

Determine the $\overline { X Y }$ - coordinates of $( - 2,5 )$ if the axes are rotated through an angle $\phi = 30 ^ { \circ }$ .

Find an equation for the conic whose graph is shown.

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Write a polar equation of a hyperbola with eccentricity $3$ and directrix $r = 2 \csc \theta$

Find the vertices of the hyperbola. $16 y ^ { 2 } - 4 x ^ { 2 } = 64$

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Find the vertices of the hyperbola. $16 y ^ { 2 } - 4 x ^ { 2 } = 64$

Find an equation for the ellipse with center at the origin, major axis of length $2 \sqrt { 7 }$ , minor axis of length $2 \sqrt { 3 }$ , and whose foci lie on the $y$ -axis.

Find the vertex, and directrix of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Find an equation for the conic whose graph is shown.

Find an equation of the parabola whose graph is shown.

Find an equation for the conic whose graph is shown.

Find an equation for the conic whose graph is shown.

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences and Series

Counting and Probability

Filters

Exam 12: Conic Sections

Find an equation for the conic whose graph is shown.

Sketch the graph of the ellipse. (x−3)29+y236=1\frac { ( x - 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 19(x−3)2​+36y2​=1

Find an equation of the parabola whose graph is shown.

Find an equation for the parabola with vertex (5,5)( 5,5 )(5,5) and directrix y−axisy - a x i sy−axis .

Find an equation for the parabola with vertex (5,5)( 5,5 )(5,5) and directrix y− axis y - \text { axis }y− axis .

Determine the XY‾\overline { X Y }XY - coordinates of (−2,5)( - 2,5 )(−2,5) if the axes are rotated through an angle ϕ=30∘\phi = 30 ^ { \circ }ϕ=30∘ .

Find an equation for the conic whose graph is shown.

Find the vertices and foci for the ellipse. y2=4−2x2y ^ { 2 } = 4 - 2 x ^ { 2 }y2=4−2x2

Write a polar equation of a hyperbola with eccentricity 333 and directrix r=2csc⁡θr = 2 \csc \thetar=2cscθ

Find the vertices of the hyperbola. 16y2−4x2=6416 y ^ { 2 } - 4 x ^ { 2 } = 6416y2−4x2=64

Find the vertices and foci for the ellipse. y2=4−2x2y ^ { 2 } = 4 - 2 x ^ { 2 }y2=4−2x2

Find the vertices of the hyperbola. 16y2−4x2=6416 y ^ { 2 } - 4 x ^ { 2 } = 6416y2−4x2=64

Find an equation for the ellipse with center at the origin, major axis of length 272 \sqrt { 7 }27​ , minor axis of length 232 \sqrt { 3 }23​ , and whose foci lie on the yyy -axis.

Find the vertex, and directrix of the parabola. y2+2y−12x+37=0y ^ { 2 } + 2 y - 12 x + 37 = 0y2+2y−12x+37=0

Find an equation for the conic whose graph is shown.

Find an equation of the parabola whose graph is shown.

Find an equation for the conic whose graph is shown.

Find an equation for the conic whose graph is shown.

Complete the square to determine the type of curve represented by the equation. x2+6x−3y2+12y=12x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12x2+6x−3y2+12y=12

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Sequences and Series

Counting and Probability

Filters

Sketch the graph of the ellipse. $\frac { ( x - 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$

Find an equation for the parabola with vertex $( 5,5 )$ and directrix $y - a x i s$ .

Find an equation for the parabola with vertex $( 5,5 )$ and directrix $y - \text { axis }$ .

Determine the $\overline { X Y }$ - coordinates of $( - 2,5 )$ if the axes are rotated through an angle $\phi = 30 ^ { \circ }$ .

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Write a polar equation of a hyperbola with eccentricity $3$ and directrix $r = 2 \csc \theta$

Find the vertices of the hyperbola. $16 y ^ { 2 } - 4 x ^ { 2 } = 64$

Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Find the vertices of the hyperbola. $16 y ^ { 2 } - 4 x ^ { 2 } = 64$

Find an equation for the ellipse with center at the origin, major axis of length $2 \sqrt { 7 }$ , minor axis of length $2 \sqrt { 3 }$ , and whose foci lie on the $y$ -axis.

Find the vertex, and directrix of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$