Question 1

Find an equation for the hyperbola that has vertices $( \pm 3,0 )$ 
and asymptotes $y = \pm 5 x$ 
.

Accepted Answer

$\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 225 } = 1$

Question 2

Find an equation of a parabola with horizontal axis and vertex at the origin that passes through the point $( - 1,5 )$

Accepted Answer

A)  $y ^ { 2 } = 20 x$ 
B)  $( y - 5 ) ^ { 2 } = x$ 
C)  $x ^ { 2 } = - 25 ( y - 1 )$ 
D)  $( x - 5 ) ^ { 2 } = - 25 y$ 
E)  $y ^ { 2 } = - 25 x$ 
A)  $y ^ { 2 } = 20 x$ 
B)  $( y - 5 ) ^ { 2 } = x$ 
C)  $x ^ { 2 } = - 25 ( y - 1 )$ 
D)  $( x - 5 ) ^ { 2 } = - 25 y$ 
E)  $y ^ { 2 } = - 25 x$ E

Question 3

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)  $x ^ { 2 } = 12 ( y + 3 )$ E

Question 4

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 5

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$

Accepted Answer

A)  $r = \frac { 7 } { 10 - 3 \sin \theta }$ 
B)  $r = \frac { 2 } { 1 - 3 \sin \theta }$ 
C)  $r = \frac { 21 } { 10 + 3 \sin \theta }$ 
D)  $r = \frac { 21 } { 10 - 3 \sin \theta }$ 
E)  $r = \frac { 21 } { 10 - 3 \cos \theta }$ 
A)  $r = \frac { 7 } { 10 - 3 \sin \theta }$ 
B)  $r = \frac { 2 } { 1 - 3 \sin \theta }$ 
C)  $r = \frac { 21 } { 10 + 3 \sin \theta }$ 
D)  $r = \frac { 21 } { 10 - 3 \sin \theta }$ 
E)  $r = \frac { 21 } { 10 - 3 \cos \theta }$

Question 6

Find the eccentricity and identify the conic given by $r= 7 / ( 1 + 3 \sin \theta )$

Accepted Answer

A)  $e = 3$
, hyperbola 
B)  $e = \frac { 3 } { 7 }$
, ellipse 
C)  $e = \frac { 7 } { 3 }$
, hyperbola 
D)  $e = 7$
, hyperbola 
E)  none of these 
A)  $e = 3$
, hyperbola 
B)  $e = \frac { 3 } { 7 }$
, ellipse 
C)  $e = \frac { 7 } { 3 }$
, hyperbola 
D)  $e = 7$
, hyperbola 
E)  none of these

Question 7

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$

Accepted Answer

A)  $r= \frac { 7 } { 10 - 3 \sin \theta }$ 
B)  $r= \frac { 2 } { 1 - 3 \sin \theta }$ 
C)  $r= \frac { 21 } { 10 + 3 \sin \theta }$ 
D)  $r = \frac { 21 } { 10 - 3 \sin \theta }$ 
E)  $r= \frac { 21 } { 10 - 3 \cos \theta }$ 
A)  $r= \frac { 7 } { 10 - 3 \sin \theta }$ 
B)  $r= \frac { 2 } { 1 - 3 \sin \theta }$ 
C)  $r= \frac { 21 } { 10 + 3 \sin \theta }$ 
D)  $r = \frac { 21 } { 10 - 3 \sin \theta }$ 
E)  $r= \frac { 21 } { 10 - 3 \cos \theta }$

Question 8

Sketch the graph of the parabola. $x ^ { 2 } + 4 x - 8 y + 36 = 0$

Accepted Answer

The answer of Sketch the graph of the parabola. \(x...

Question 9

Find the eccentricity and identify the conic given by $r= \frac { 2 } { 1 - \cos \theta }$ 
.

Accepted Answer

@#LAT-DLM& 
, so the

Question 10

Find the foci of the hyperbola. $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$

Accepted Answer

The answer of Find the foci of the hyperbola. \(\frac...

Question 11

Sketch the graph of the parabola. $$x ^ { 2 } + 2 y = 0$$

Accepted Answer

The answer of Sketch the graph of the parabola. \[x...

Question 12

Find an equation of the parabola whose graph is shown.

Accepted Answer

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

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

A)  $\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 7 } = 1$ 
B)  $\frac { x ^ { 2 } } { 12 } + \frac { y ^ { 2 } } { 14 } = 1$ 
C)  $\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 12 } = 1$ 
D)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 3 } = 1$ 
E)  none of these 
A)  $\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 7 } = 1$ 
B)  $\frac { x ^ { 2 } } { 12 } + \frac { y ^ { 2 } } { 14 } = 1$ 
C)  $\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 12 } = 1$ 
D)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 3 } = 1$ 
E)  none of these

Question 14

Find the vertex, focus, and directrix of the parabola $x ^ { 2 } = 7 y$

Accepted Answer

A)  $V ( 0,7 ) , F ( 0,7 ) , x = - 7$ 
B)  $V ( 7,0 ) , F \left( \frac { 7 } { 4 } , 0 \right) , y = \frac { 7 } { 4 }$ 
C)  $V ( 0,0 ) , F \left( 0 , - \frac { 7 } { 4 } \right) , x = \frac { 7 } { 4 }$ 
D)  $V ( 0,0 ) , F \left( 0 , \frac { 7 } { 4 } \right) , y = - \frac { 7 } { 4 }$ 
E)  $V \left( 0 , \frac { 7 } { 4 } \right) , F \left( 0 , \frac { 7 } { 4 } \right) , y = - \frac { 7 } { 4 }$ 
A)  $V ( 0,7 ) , F ( 0,7 ) , x = - 7$ 
B)  $V ( 7,0 ) , F \left( \frac { 7 } { 4 } , 0 \right) , y = \frac { 7 } { 4 }$ 
C)  $V ( 0,0 ) , F \left( 0 , - \frac { 7 } { 4 } \right) , x = \frac { 7 } { 4 }$ 
D)  $V ( 0,0 ) , F \left( 0 , \frac { 7 } { 4 } \right) , y = - \frac { 7 } { 4 }$ 
E)  $V \left( 0 , \frac { 7 } { 4 } \right) , F \left( 0 , \frac { 7 } { 4 } \right) , y = - \frac { 7 } { 4 }$

Question 15

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)  none 
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)  none

Question 16

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 17

Find an equation for the conic whose graph is shown.

Accepted Answer

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

Question 18

Find an equation for the ellipse with foci $( \pm 7,0 )$ 
, and major axis of length $18$ 
.

Accepted Answer

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

Question 19

Sketch the graph of the parabola. $x ^ { 2 } + 2 y = 0$

Accepted Answer

The answer of Sketch the graph of the parabola. \(x...

Question 20

Find an equation of the parabola whose graph is shown.

Accepted Answer

A)  $x ^ { 2 } = 4 y$ 
B)  $x ^ { 2 } = 16 y$ 
C)  $y ^ { 2 } = 16 x$ 
D)  $y ^ { 2 } = 8 x$ 
E)  none of these 
A)  $x ^ { 2 } = 4 y$ 
B)  $x ^ { 2 } = 16 y$ 
C)  $y ^ { 2 } = 16 x$ 
D)  $y ^ { 2 } = 8 x$ 
E)  none of these

Find an equation for the hyperbola that has vertices $( \pm 3,0 )$ and asymptotes $y = \pm 5 x$ .

Find an equation of a parabola with horizontal axis and vertex at the origin that passes through the point $( - 1,5 )$

Find an equation for the conic whose graph is shown.

Find an equation for the conic whose graph is shown.

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$

Find the eccentricity and identify the conic given by $r= 7 / ( 1 + 3 \sin \theta )$

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$

Sketch the graph of the parabola. $x ^ { 2 } + 4 x - 8 y + 36 = 0$

Find the eccentricity and identify the conic given by $r= \frac { 2 } { 1 - \cos \theta }$ .

Find the foci of the hyperbola. $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$

Sketch the graph of the parabola. $x ^ { 2 } + 2 y = 0$

Find an equation of the parabola whose graph is shown.

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, focus, and directrix of the parabola $x ^ { 2 } = 7 y$

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. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Find an equation for the conic whose graph is shown.

Find an equation for the ellipse with foci $( \pm 7,0 )$ , and major axis of length $18$ .

Sketch the graph of the parabola. $x ^ { 2 } + 2 y = 0$

Find an equation of the parabola whose graph is shown.

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 hyperbola that has vertices (±3,0)( \pm 3,0 )(±3,0) and asymptotes y=±5xy = \pm 5 xy=±5x .

Find an equation of a parabola with horizontal axis and vertex at the origin that passes through the point (−1,5)( - 1,5 )(−1,5)

Find an equation for the conic whose graph is shown.

Find an equation for the conic whose graph is shown.

Write a polar equation of an ellipse with eccentricity 0.30.30.3 and directrix y=−7y = - 7y=−7

Find the eccentricity and identify the conic given by r=7/(1+3sin⁡θ)r= 7 / ( 1 + 3 \sin \theta )r=7/(1+3sinθ)

Write a polar equation of an ellipse with eccentricity 0.30.30.3 and directrix y=−7y = - 7y=−7

Sketch the graph of the parabola. x2+4x−8y+36=0x ^ { 2 } + 4 x - 8 y + 36 = 0x2+4x−8y+36=0

Find the eccentricity and identify the conic given by r=21−cos⁡θr= \frac { 2 } { 1 - \cos \theta }r=1−cosθ2​ .

Find the foci of the hyperbola. y216−x29=1\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 116y2​−9x2​=1

Sketch the graph of the parabola. x2+2y=0x ^ { 2 } + 2 y = 0x2+2y=0

Find an equation of the parabola whose graph is shown.

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, focus, and directrix of the parabola x2=7yx ^ { 2 } = 7 yx2=7y

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

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

Find an equation for the conic whose graph is shown.

Find an equation for the ellipse with foci (±7,0)( \pm 7,0 )(±7,0) , and major axis of length 181818 .

Sketch the graph of the parabola. x2+2y=0x ^ { 2 } + 2 y = 0x2+2y=0

Find an equation of the parabola whose graph is shown.

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

Find an equation for the hyperbola that has vertices $( \pm 3,0 )$ and asymptotes $y = \pm 5 x$ .

Find an equation of a parabola with horizontal axis and vertex at the origin that passes through the point $( - 1,5 )$

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$

Find the eccentricity and identify the conic given by $r= 7 / ( 1 + 3 \sin \theta )$

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$

Sketch the graph of the parabola. $x ^ { 2 } + 4 x - 8 y + 36 = 0$

Find the eccentricity and identify the conic given by $r= \frac { 2 } { 1 - \cos \theta }$ .

Find the foci of the hyperbola. $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 9 } = 1$

Sketch the graph of the parabola. $x ^ { 2 } + 2 y = 0$

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, focus, and directrix of the parabola $x ^ { 2 } = 7 y$

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. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Find an equation for the ellipse with foci $( \pm 7,0 )$ , and major axis of length $18$ .

Sketch the graph of the parabola. $x ^ { 2 } + 2 y = 0$