Question 1

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation.  $r = \frac { 2 e } { 1 - e \sin \theta }$

Accepted Answer

A)  $r = \frac { 2 } { 1 - \sin \theta } \Rightarrow \text { parabola }$ 
B)  $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$ 
C)  $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { hyperbola }$ 
D)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$ 
A)  $r = \frac { 2 } { 1 - \sin \theta } \Rightarrow \text { parabola }$ 
B)  $r = \frac { 1 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$ 
C)  $r = \frac { 2 } { 1 - 2 \sin \theta } \Rightarrow \text { hyperbola }$ 
D)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { parabola }$ 
E)  $r = \frac { 2 } { 1 + \sin \theta } \Rightarrow \text { hyperbola }$

Question 2

Find the center and the vertices which located on the major axis of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Accepted Answer

A) center: (0, 0) vertices: (-9, 0), (9, 0) 
B) center: (0, 0) vertices: (0, -9), (0, 9) 
C) center: (-9, 9) vertices: (-1, 0), (1, 0) 
D) center: (0, 0) vertices: (-9, -1), (9, 1) 
E) center: (-9, 9) vertices: (-1, -9), (1, 9) 
A) center: (0, 0) vertices: (-9, 0), (9, 0) 
B) center: (0, 0) vertices: (0, -9), (0, 9) 
C) center: (-9, 9) vertices: (-1, 0), (1, 0) 
D) center: (0, 0) vertices: (-9, -1), (9, 1) 
E) center: (-9, 9) vertices: (-1, -9), (1, 9)

Question 3

Find the equation of the parabola so that its graph matches the description.  $( y + 2 ) ^ { 2 } = 3 ( x - 7 )$ ; lower half of parabola

Accepted Answer

A)  $y = - 2 + \sqrt { 3 ( x - 7 ) }$ 
B)  $y = - 2 - \sqrt { 3 ( x - 7 ) }$ 
C)  $x = - 2 + \sqrt { 3 ( y - 7 ) }$ 
D)  $x = - 2 - \sqrt { 3 ( y - 7 ) }$ 
E)  $x = - 2 + \sqrt { 3 ( y + 7 ) }$ 
A)  $y = - 2 + \sqrt { 3 ( x - 7 ) }$ 
B)  $y = - 2 - \sqrt { 3 ( x - 7 ) }$ 
C)  $x = - 2 + \sqrt { 3 ( y - 7 ) }$ 
D)  $x = - 2 - \sqrt { 3 ( y - 7 ) }$ 
E)  $x = - 2 + \sqrt { 3 ( y + 7 ) }$

Question 4

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $x ^ { 2 } + y ^ { 2 } - 7 x + 2 y - 12 = 0$

Accepted Answer

A) Parabola 
B) Hyperbola 
C) Ellipse 
D) Circle 
E) None of the above 
A) Parabola 
B) Hyperbola 
C) Ellipse 
D) Circle 
E) None of the above

Question 5

The Comet Borrelly has an elliptical orbit with an eccentricity of  $e \approx 0.624$ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Accepted Answer

A)  $\frac { 1.780 } { 1 - 1.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
B)  $\frac { 1.780 } { 1 + \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
C)  $\frac { 0.624 } { 1 + 1.780 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
D)  $\frac { 1.780 } { 1 + 0.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
E)  $\overline { 1 - 1.624 \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
A)  $\frac { 1.780 } { 1 - 1.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
B)  $\frac { 1.780 } { 1 + \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
C)  $\frac { 0.624 } { 1 + 1.780 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
D)  $\frac { 1.780 } { 1 + 0.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit. 
E)  $\overline { 1 - 1.624 \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.

Question 6

Select the graph for following equation.  $\frac { x ^ { 2 } } { 9 } + y ^ { 2 } = 1$

Accepted Answer

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

Question 7

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x } { 4 } + \frac { y } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 16 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x } { 4 } + \frac { y } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 8

The path of a projectile projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is $x ^ { 2 } = - \frac { v ^ { 2 } } { 16 } ( y - s )$ .In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels.A ball is thrown from the top of a 150-foot tower with a velocity of 32 feet per second.Find the equation of the parabolic path.

Accepted Answer

A)  $x ^ { 2 } = - 32 ( y - 150 )$ 
B)  $x ^ { 2 } = 64 ( y - 150 )$ 
C)  $x ^ { 2 } = 1406 ( y - 32 )$ 
D)  $x ^ { 2 } = - 1406 ( y - 32 )$ 
E)  $x ^ { 2 } = - 64 ( y - 150 )$ 
A)  $x ^ { 2 } = - 32 ( y - 150 )$ 
B)  $x ^ { 2 } = 64 ( y - 150 )$ 
C)  $x ^ { 2 } = 1406 ( y - 32 )$ 
D)  $x ^ { 2 } = - 1406 ( y - 32 )$ 
E)  $x ^ { 2 } = - 64 ( y - 150 )$

Question 9

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = \frac { 4 } { \sin \theta - 2 \cos \theta }$

Accepted Answer

A)  $y = 2 x + 4 \Rightarrow \text { Line }$    
B)  $y = 2 x + 4 \Rightarrow \text { Line }$    
C)  $y = 2 x + 4 \Rightarrow \text { Line }$    
D)  $y = 2 x + 4 \Rightarrow \text { Line }$    
E)  $y = 2 x + 4 \Rightarrow \text { Line }$    
A)  $y = 2 x + 4 \Rightarrow \text { Line }$    
B)  $y = 2 x + 4 \Rightarrow \text { Line }$    
C)  $y = 2 x + 4 \Rightarrow \text { Line }$    
D)  $y = 2 x + 4 \Rightarrow \text { Line }$    
E)  $y = 2 x + 4 \Rightarrow \text { Line }$

Question 10

Select the correct equation of the following graph.

Accepted Answer

A)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 49 } = 1$ 
B)  $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$ 
A)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 49 } = 1$ 
B)  $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 49 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$

Question 11

Select the polar equation of graph.

Accepted Answer

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

Question 12

The graph of the equation $x ^ { 2 } + x y + k y ^ { 2 } + 12 x + 16 = 0$ where, $k$ is any constant less than $\frac { 1 } { 4 }$ , is a hyperbola.

Accepted Answer

A) True 
 B)False

Question 13

Find the vertex and focus of the parabola. $( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0$

Accepted Answer

A) vertex: $( 3,7 )$ focus: $( 3,7 )$ 
B) vertex: $( 3,7 )$ focus: $( - 9 , - 3 )$ 
C) vertex: $( 3,7 )$ focus: $( 3,23 )$ 
D) vertex: $( - 3 , - 7 )$ focus: $( - 3 , + 7 )$ 
E) vertex: $( - 3 , - 7 )$ focus: $( 1 , - 7 )$ 
A) vertex: $( 3,7 )$ focus: $( 3,7 )$ 
B) vertex: $( 3,7 )$ focus: $( - 9 , - 3 )$ 
C) vertex: $( 3,7 )$ focus: $( 3,23 )$ 
D) vertex: $( - 3 , - 7 )$ focus: $( - 3 , + 7 )$ 
E) vertex: $( - 3 , - 7 )$ focus: $( 1 , - 7 )$

Question 14

Find the standard form of the equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 7 } { 9 }$ .

Accepted Answer

A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 32 } = 1$ 
D)  $\frac { x ^ { 2 } } { 32 } + \frac { y ^ { 2 } } { 81 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 81 } = 1$ 
A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 32 } = 1$ 
D)  $\frac { x ^ { 2 } } { 32 } + \frac { y ^ { 2 } } { 81 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 81 } = 1$

Question 15

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = \frac { \pi } { 4 }$

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $\frac { \pi } { 4 }$

Question 16

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m.

Accepted Answer

A)  $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
B)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$ 
C)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
D)  $\frac { 7 | m + 7 | } { \sqrt { m ^ { 2 } + 1 } }$ 
E)  $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
A)  $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
B)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$ 
C)  $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
D)  $\frac { 7 | m + 7 | } { \sqrt { m ^ { 2 } + 1 } }$ 
E)  $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$

Question 17

Find the vertices and asymptotes of the hyperbola.  $16 y ^ { 2 } - 9 x ^ { 2 } = 144$

Accepted Answer

A) vertices: (0, ±3) asymptote: $y = \pm \frac { 3 } { 4 } x$ 
B) vertices: (0, ±3) asymptote: $y = \pm \frac { 4 } { 3 } x$ 
C) vertices: (±3, 0) asymptote: $y = \pm \frac { 3 } { 4 } x$ 
D) vertices: (±3, 0) asymptote: $y = \pm \frac { 4 } { 3 } x$ 
E) vertices: (±3, 4) asymptote: $y = \pm \frac { 3 } { 4 } x$ 
A) vertices: (0, ±3) asymptote: $y = \pm \frac { 3 } { 4 } x$ 
B) vertices: (0, ±3) asymptote: $y = \pm \frac { 4 } { 3 } x$ 
C) vertices: (±3, 0) asymptote: $y = \pm \frac { 3 } { 4 } x$ 
D) vertices: (±3, 0) asymptote: $y = \pm \frac { 4 } { 3 } x$ 
E) vertices: (±3, 4) asymptote: $y = \pm \frac { 3 } { 4 } x$

Question 18

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 
Vertices: $( 0 , \pm 8 )$ ; Foci: $( 0 , \pm 4 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 48 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 48 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$ 
A)  $\frac { x ^ { 2 } } { 48 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 4 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 48 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 48 } = 1$

Question 19

Find the Eccentricity of the conic.  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$

Accepted Answer

A) Eccentricity: $e = \frac { \sqrt { 48 } } { 64 }$ 
B) Eccentricity: $e = \frac { \sqrt { 48 } } { 4 }$ 
C) Eccentricity: $e = \frac { \sqrt { 64 } } { 4 }$ 
D) Eccentricity: $e = \frac { \sqrt { 48 } } { 8 }$ 
E) Eccentricity: $e = \frac { \sqrt { 48 } } { 48 }$ 
A) Eccentricity: $e = \frac { \sqrt { 48 } } { 64 }$ 
B) Eccentricity: $e = \frac { \sqrt { 48 } } { 4 }$ 
C) Eccentricity: $e = \frac { \sqrt { 64 } } { 4 }$ 
D) Eccentricity: $e = \frac { \sqrt { 48 } } { 8 }$ 
E) Eccentricity: $e = \frac { \sqrt { 48 } } { 48 }$

Question 20

Select correct graph to graph rotated conic. $r = \frac { 6 } { 1 - \cos ( \theta - \pi / 4 ) }$

Accepted Answer

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

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. $r = \frac { 2 e } { 1 - e \sin \theta }$

Find the center and the vertices which located on the major axis of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Find the equation of the parabola so that its graph matches the description. $( y + 2 ) ^ { 2 } = 3 ( x - 7 )$ ; lower half of parabola

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 7 x + 2 y - 12 = 0$

The Comet Borrelly has an elliptical orbit with an eccentricity of $e \approx 0.624$ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Select the graph for following equation. $\frac { x ^ { 2 } } { 9 } + y ^ { 2 } = 1$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { 4 } { \sin \theta - 2 \cos \theta }$

Select the correct equation of the following graph.

Select the polar equation of graph.

The graph of the equation $x ^ { 2 } + x y + k y ^ { 2 } + 12 x + 16 = 0$ where, $k$ is any constant less than $\frac { 1 } { 4 }$ , is a hyperbola.

Find the vertex and focus of the parabola. $( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0$

Find the standard form of the equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 7 } { 9 }$ .

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { \pi } { 4 }$

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m.

Find the vertices and asymptotes of the hyperbola. $16 y ^ { 2 } - 9 x ^ { 2 } = 144$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: $( 0 , \pm 8 )$ ; Foci: $( 0 , \pm 4 )$

Find the Eccentricity of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$

Select correct graph to graph rotated conic. $r = \frac { 6 } { 1 - \cos ( \theta - \pi / 4 ) }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 10: Topics In Analytic Geometry

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. r=2e1−esin⁡θr = \frac { 2 e } { 1 - e \sin \theta }r=1−esinθ2e​

Find the center and the vertices which located on the major axis of the ellipse. 81x2+y2=8181 x ^ { 2 } + y ^ { 2 } = 8181x2+y2=81

Find the equation of the parabola so that its graph matches the description. (y+2)2=3(x−7)( y + 2 ) ^ { 2 } = 3 ( x - 7 )(y+2)2=3(x−7) ; lower half of parabola

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2+y2−7x+2y−12=0x ^ { 2 } + y ^ { 2 } - 7 x + 2 y - 12 = 0x2+y2−7x+2y−12=0

The Comet Borrelly has an elliptical orbit with an eccentricity of e≈0.624e \approx 0.624e≈0.624 .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Select the graph for following equation. x29+y2=1\frac { x ^ { 2 } } { 9 } + y ^ { 2 } = 19x2​+y2=1

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=4sin⁡θ−2cos⁡θr = \frac { 4 } { \sin \theta - 2 \cos \theta }r=sinθ−2cosθ4​

Select the correct equation of the following graph.

Select the polar equation of graph.

The graph of the equation x2+xy+ky2+12x+16=0x ^ { 2 } + x y + k y ^ { 2 } + 12 x + 16 = 0x2+xy+ky2+12x+16=0 where, kkk is any constant less than 14\frac { 1 } { 4 }41​ , is a hyperbola.

Find the vertex and focus of the parabola. (y+7)2−16(x+3)=0( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0(y+7)2−16(x+3)=0

Find the standard form of the equation of the ellipse with vertices (±9,0)( \pm 9,0 )(±9,0) and eccentricity e=79e = \frac { 7 } { 9 }e=97​ .

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=π4r = \frac { \pi } { 4 }r=4π​

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m.

Find the vertices and asymptotes of the hyperbola. 16y2−9x2=14416 y ^ { 2 } - 9 x ^ { 2 } = 14416y2−9x2=144

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0,±8)( 0 , \pm 8 )(0,±8) ; Foci: (0,±4)( 0 , \pm 4 )(0,±4)

Find the Eccentricity of the conic. x264+y216=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 164x2​+16y2​=1

Select correct graph to graph rotated conic. r=61−cos⁡(θ−π/4)r = \frac { 6 } { 1 - \cos ( \theta - \pi / 4 ) }r=1−cos(θ−π/4)6​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Select the polar equation of the conic for e = 1.0 and identify the conic for the following equation. $r = \frac { 2 e } { 1 - e \sin \theta }$

Find the center and the vertices which located on the major axis of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Find the equation of the parabola so that its graph matches the description. $( y + 2 ) ^ { 2 } = 3 ( x - 7 )$ ; lower half of parabola

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } + y ^ { 2 } - 7 x + 2 y - 12 = 0$

The Comet Borrelly has an elliptical orbit with an eccentricity of $e \approx 0.624$ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Select the graph for following equation. $\frac { x ^ { 2 } } { 9 } + y ^ { 2 } = 1$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { 4 } { \sin \theta - 2 \cos \theta }$

The graph of the equation $x ^ { 2 } + x y + k y ^ { 2 } + 12 x + 16 = 0$ where, $k$ is any constant less than $\frac { 1 } { 4 }$ , is a hyperbola.

Find the vertex and focus of the parabola. $( y + 7 ) ^ { 2 } - 16 ( x + 3 ) = 0$

Find the standard form of the equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 7 } { 9 }$ .

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = \frac { \pi } { 4 }$

Find the vertices and asymptotes of the hyperbola. $16 y ^ { 2 } - 9 x ^ { 2 } = 144$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: $( 0 , \pm 8 )$ ; Foci: $( 0 , \pm 4 )$

Find the Eccentricity of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 16 } = 1$

Select correct graph to graph rotated conic. $r = \frac { 6 } { 1 - \cos ( \theta - \pi / 4 ) }$