Question 1

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

Accepted Answer

A)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { 2 + 5 \sqrt { 3 } } { 2 }$ 
B)  $X = \frac { 2 \sqrt { 3 } } { 2 }$
, $Y = 1 - \frac { 5 \sqrt { 3 } } { 2 }$ 
C)  $X = 5 - 2 \sqrt { 3 }$
, $Y = 1 + \frac { \sqrt { 3 } } { 2 }$ 
D)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { \sqrt { 3 } + 5 } { 2 }$ 
E)  $X = \frac { 1 + 2 \sqrt { 3 } } { 2 }$
, $Y = - 5 + \frac { \sqrt { 3 } } { 2 }$ 
A)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { 2 + 5 \sqrt { 3 } } { 2 }$ 
B)  $X = \frac { 2 \sqrt { 3 } } { 2 }$
, $Y = 1 - \frac { 5 \sqrt { 3 } } { 2 }$ 
C)  $X = 5 - 2 \sqrt { 3 }$
, $Y = 1 + \frac { \sqrt { 3 } } { 2 }$ 
D)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { \sqrt { 3 } + 5 } { 2 }$ 
E)  $X = \frac { 1 + 2 \sqrt { 3 } } { 2 }$
, $Y = - 5 + \frac { \sqrt { 3 } } { 2 }$

Question 2

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

Accepted Answer

A)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { 2 + 5 \sqrt { 3 } } { 2 }$ 
B)  $X = \frac { 2 \sqrt { 3 } } { 2 }$
, $Y = 1 - \frac { 5 \sqrt { 3 } } { 2 }$ 
C)  $X = 5 - 2 \sqrt { 3 }$
, $Y = 1 + \frac { \sqrt { 3 } } { 2 }$ 
D)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { \sqrt { 3 } + 5 } { 2 }$ 
E)  $X = \frac { 1 + 2 \sqrt { 3 } } { 2 }$
, $Y = - 5 + \frac { \sqrt { 3 } } { 2 }$ 
A)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { 2 + 5 \sqrt { 3 } } { 2 }$ 
B)  $X = \frac { 2 \sqrt { 3 } } { 2 }$
, $Y = 1 - \frac { 5 \sqrt { 3 } } { 2 }$ 
C)  $X = 5 - 2 \sqrt { 3 }$
, $Y = 1 + \frac { \sqrt { 3 } } { 2 }$ 
D)  $X = \frac { 5 - 2 \sqrt { 3 } } { 2 }$
, $Y = \frac { \sqrt { 3 } + 5 } { 2 }$ 
E)  $X = \frac { 1 + 2 \sqrt { 3 } } { 2 }$
, $Y = - 5 + \frac { \sqrt { 3 } } { 2 }$

Question 3

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 4

Find an equation of the parabola whose graph is shown.

Accepted Answer

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

Question 5

Find an equation for parabola with vertex $( - 1,3 )$ 
and directrix $x = - 4$ 
.

Accepted Answer

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

Question 6

Sketch the graph of the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

Accepted Answer

@#LAT-DLM& 
, Center: @#LAT-DLM& 
, foci

Question 7

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

Accepted Answer

A)  major axis: $14$
, minor: $2 \sqrt { 13 }$ 
B)  major axis: $7$
, minor: $2 \sqrt { 14 }$ 
C)  major axis: $49$
, minor: $2 \sqrt { 13 }$ 
D)  major axis: $14$
, minor: $14$ 
E)  none of these 
A)  major axis: $14$
, minor: $2 \sqrt { 13 }$ 
B)  major axis: $7$
, minor: $2 \sqrt { 14 }$ 
C)  major axis: $49$
, minor: $2 \sqrt { 13 }$ 
D)  major axis: $14$
, minor: $14$ 
E)  none of these

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

The answer of Write a polar equation of an ellipse...

Question 10

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 11

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 12

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

Question 13

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

Accepted Answer

The answer of Complete the square to determine the type...

Question 14

Find the vertices and foci for the ellipse. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$

Accepted Answer

Vertices:

Question 15

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 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

The answer of Complete the square to determine the type...

Question 17

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

Accepted Answer

@#LAT-DLM& 
, so the

Question 18

Sketch the graph of the ellipse. $$\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)    
B)    
C) 
  
D) 
  
E) none of these 
A)    
B)    
C) 
  
D) 
  
E) none of these

Question 19

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

Accepted Answer

The answer of Sketch the graph of the parabola. \[2...

Question 20

Find an equation for the conic whose graph is shown.

Accepted Answer

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

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

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. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Find an equation of the parabola whose graph is shown.

Find an equation for parabola with vertex $( - 1,3 )$ and directrix $x = - 4$ .

Sketch the graph of the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

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

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

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

Find an equation for the conic whose graph is shown.

Find an equation of the parabola whose graph is shown.

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

Find the vertices and foci for the ellipse. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$

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

Sketch the graph of the ellipse. $\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$

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

Find an equation for the conic 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

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Exam 12: Conic Sections

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∘

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

Find an equation of the parabola whose graph is shown.

Find an equation for parabola with vertex (−1,3)( - 1,3 )(−1,3) and directrix x=−4x = - 4x=−4 .

Sketch the graph of the hyperbola. y2−2y−4x2−16x=15y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15y2−2y−4x2−16x=15

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

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

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

Find an equation for the conic whose graph is shown.

Find an equation of the parabola whose graph is shown.

Complete the square to determine the type of curve represented by the equation. 4x2+9y2−16x−20=04 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 04x2+9y2−16x−20=0

Find the vertices and foci for the ellipse. 4x2+9y2=364 x ^ { 2 } + 9 y ^ { 2 } = 364x2+9y2=36

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

Sketch the graph of the ellipse. (x−5)236+y29=1\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 136(x−5)2​+9y2​=1

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

Find an equation for the conic 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

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

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. $y ^ { 2 } = 4 - 2 x ^ { 2 }$

Find an equation for parabola with vertex $( - 1,3 )$ and directrix $x = - 4$ .

Sketch the graph of the hyperbola. $y ^ { 2 } - 2 y - 4 x ^ { 2 } - 16 x = 15$

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

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

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

Complete the square to determine the type of curve represented by the equation. $4 x ^ { 2 } + 9 y ^ { 2 } - 16 x - 20 = 0$

Find the vertices and foci for the ellipse. $4 x ^ { 2 } + 9 y ^ { 2 } = 36$

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

Sketch the graph of the ellipse. $\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$

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