Question 1

Sketch the graph of the parabola. $2 x + 7 y ^ { 2 } = 0$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

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

Accepted Answer

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

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 conic whose graph is shown.

Accepted Answer

From the graph, @#LAT-DLM&  , @#LAT-DLM& 
, and th

Question 5

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

Accepted Answer

A)  $V ( 6 , - 1 )$ 
B)  $V ( - 2,4 )$ 
C)  $V ( 5 , - 2 )$ 
D)  $V ( - 2 , - 6 )$ 
E)  $V ( - 2,8 )$ 
A)  $V ( 6 , - 1 )$ 
B)  $V ( - 2,4 )$ 
C)  $V ( 5 , - 2 )$ 
D)  $V ( - 2 , - 6 )$ 
E)  $V ( - 2,8 )$

Question 6

Find the lengths of the major and minor axes for the ellipse. $25 x ^ { 2 } + y ^ { 2 } = 25$

Accepted Answer

A)  major axis: $5$
, minor: $2$ 
B)  major axis: $5$
, minor: $\sqrt { 5 }$ 
C)  major axis: $25$
, minor: $2 \sqrt { 10 }$ 
D)  major axis: $10$
, minor: $2$ 
E)  none of these 
A)  major axis: $5$
, minor: $2$ 
B)  major axis: $5$
, minor: $\sqrt { 5 }$ 
C)  major axis: $25$
, minor: $2 \sqrt { 10 }$ 
D)  major axis: $10$
, minor: $2$ 
E)  none of these

Question 7

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 800 ft from the cannon and the highest point it reaches is 1600 ft above the ground, find an equation for the path of the cannonball. Place the origin at the location of the cannon.

Accepted Answer

The answer of A cannon fires a cannonball as shown...

Question 8

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 9

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 10

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

Accepted Answer

The answer of Determine the $X Y$ 
- coordinates of...

Question 11

Find the lengths of the major and minor axes for the ellipse. $25 x ^ { 2 } + y ^ { 2 } = 25$

Accepted Answer

Length of

Question 12

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = - 3$

Accepted Answer

The answer of Write a polar equation of a conic...

Question 13

Sketch the graph of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Accepted Answer

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

Question 14

Find the foci of the hyperbola. $x ^ { 2 } - 5 y ^ { 2 } - 10 = 0$

Accepted Answer

A)  $F ( \pm 5,0 )$ 
B)  $F ( \pm 2 \sqrt { 3 } , 0 )$ 
C)  $F ( 0 , \pm 2 \sqrt { 3 } )$ 
D)  $F ( 0 , \pm \sqrt { 6 } )$ 
E)  $F ( 0 , \pm \sqrt { 3 } )$ 
A)  $F ( \pm 5,0 )$ 
B)  $F ( \pm 2 \sqrt { 3 } , 0 )$ 
C)  $F ( 0 , \pm 2 \sqrt { 3 } )$ 
D)  $F ( 0 , \pm \sqrt { 6 } )$ 
E)  $F ( 0 , \pm \sqrt { 3 } )$

Question 15

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

The answer of A cannon fires a cannonball as shown...

Question 16

Find the lengths of the major and minor axes for the ellipse. $\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 1$

Accepted Answer

Length of

Question 17

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

Accepted Answer

The answer of Write a polar equation of a hyperbola...

Question 18

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = 3$

Accepted Answer

A)  $r = \frac { 3 } { 1 - \sin \theta }$ 
B)  $r = \frac { 1 / 3 } { 1 + \sin \theta }$ 
C)  $r= \frac { 3 } { 1 + \cos \theta }$ 
D)  $r = \frac { 3 } { 1 - \cos \theta }$ 
E)  none of these 
A)  $r = \frac { 3 } { 1 - \sin \theta }$ 
B)  $r = \frac { 1 / 3 } { 1 + \sin \theta }$ 
C)  $r= \frac { 3 } { 1 + \cos \theta }$ 
D)  $r = \frac { 3 } { 1 - \cos \theta }$ 
E)  none of these

Question 19

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

Accepted Answer

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

Question 20

Find the foci for the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

Accepted Answer

A)  $F ( 0,1 \pm \sqrt { 5 } )$ 
B)  $F ( - 1,2 \pm \sqrt { 5 } )$ 
C)  $F ( - 1,5 \pm \sqrt { 5 } )$ 
D)  $F ( 2,1 \pm \sqrt { 5 } )$ 
E)  none 
A)  $F ( 0,1 \pm \sqrt { 5 } )$ 
B)  $F ( - 1,2 \pm \sqrt { 5 } )$ 
C)  $F ( - 1,5 \pm \sqrt { 5 } )$ 
D)  $F ( 2,1 \pm \sqrt { 5 } )$ 
E)  none

Sketch the graph of the parabola. $2 x + 7 y ^ { 2 } = 0$

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

Find an equation of the parabola whose graph is shown.

Find an equation for the conic whose graph is shown.

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

Find the lengths of the major and minor axes for the ellipse. $25 x ^ { 2 } + y ^ { 2 } = 25$

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

Find an equation for the conic whose graph is shown.

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

Find the lengths of the major and minor axes for the ellipse. $25 x ^ { 2 } + y ^ { 2 } = 25$

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = - 3$

Sketch the graph of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Find the foci of the hyperbola. $x ^ { 2 } - 5 y ^ { 2 } - 10 = 0$

Find the lengths of the major and minor axes for the ellipse. $\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 1$

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

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = 3$

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

Find the foci for the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

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

Sketch the graph of the parabola. 2x+7y2=02 x + 7 y ^ { 2 } = 02x+7y2=0

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

Find an equation of the parabola whose graph is shown.

Find an equation for the conic whose graph is shown.

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

Find the lengths of the major and minor axes for the ellipse. 25x2+y2=2525 x ^ { 2 } + y ^ { 2 } = 2525x2+y2=25

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 for the conic whose graph is shown.

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

Find the lengths of the major and minor axes for the ellipse. 25x2+y2=2525 x ^ { 2 } + y ^ { 2 } = 2525x2+y2=25

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix y=−3y = - 3y=−3

Sketch the graph of the parabola. y2+2y−12x+37=0y ^ { 2 } + 2 y - 12 x + 37 = 0y2+2y−12x+37=0

Find the foci of the hyperbola. x2−5y2−10=0x ^ { 2 } - 5 y ^ { 2 } - 10 = 0x2−5y2−10=0

Find the lengths of the major and minor axes for the ellipse. x213+y249=1\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 113x2​+49y2​=1

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

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix y=3y = 3y=3

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

Find the foci for the hyperbola. y2−2y−4x2−16x=15y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15y2−2y−4x2−16x=15

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 parabola. $2 x + 7 y ^ { 2 } = 0$

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

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

Find the lengths of the major and minor axes for the ellipse. $25 x ^ { 2 } + y ^ { 2 } = 25$

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

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

Find the lengths of the major and minor axes for the ellipse. $25 x ^ { 2 } + y ^ { 2 } = 25$

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = - 3$

Sketch the graph of the parabola. $y ^ { 2 } + 2 y - 12 x + 37 = 0$

Find the foci of the hyperbola. $x ^ { 2 } - 5 y ^ { 2 } - 10 = 0$

Find the lengths of the major and minor axes for the ellipse. $\frac { x ^ { 2 } } { 13 } + \frac { y ^ { 2 } } { 49 } = 1$

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

Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions.Parabola, directrix $y = 3$

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

Find the foci for the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$