Question 1

Identify the conic and select its correct graph.  $r = \frac { 3 } { 2 + 6 \sin \theta }$

Accepted Answer

A)  $e = 3 > 1 \Rightarrow$ Hyperbola   
B)  $e = 3 > 1 \Rightarrow$ Hyperbola   
C)  $e = 3 > 1 \Rightarrow$ H  
D)  $e = 3 > 1 \Rightarrow$ Hyperbola   
E)  $e = 3 > 1 \Rightarrow$ Hyperbola   
A)  $e = 3 > 1 \Rightarrow$ Hyperbola   
B)  $e = 3 > 1 \Rightarrow$ Hyperbola   
C)  $e = 3 > 1 \Rightarrow$ H  
D)  $e = 3 > 1 \Rightarrow$ Hyperbola   
E)  $e = 3 > 1 \Rightarrow$ Hyperbola

Question 2

Identify the conic by writing the equation in standard form. $8 x ^ { 2 } + 8 y ^ { 2 } + 32 x + 144 y + 520 = 0$

Accepted Answer

A)  $\frac { ( x + 2 ) ^ { 2 } } { \frac { 69 } { 8 } } + \frac { ( y + 9 ) ^ { 2 } } { \frac { 69 } { 8 } } = 1$ ; ellipse 
B)  $\frac { ( x + 2 ) ^ { 2 } } { \frac { 11 } { 8 } } + \frac { ( y + 9 ) ^ { 2 } } { \frac { 11 } { 8 } } = 1$ ; ellipse 
C)  $( 8 x + 2 ) ^ { 2 } + ( 8 y + 9 ) ^ { 2 } = 320$ ; circle 
D)  $( x + 2 ) ^ { 2 } + ( y + 9 ) ^ { 2 } = 40$ ; circle 
E)  $( x + 2 ) ^ { 2 } + ( y + 9 ) ^ { 2 } = 20$ ; circle 
A)  $\frac { ( x + 2 ) ^ { 2 } } { \frac { 69 } { 8 } } + \frac { ( y + 9 ) ^ { 2 } } { \frac { 69 } { 8 } } = 1$ ; ellipse 
B)  $\frac { ( x + 2 ) ^ { 2 } } { \frac { 11 } { 8 } } + \frac { ( y + 9 ) ^ { 2 } } { \frac { 11 } { 8 } } = 1$ ; ellipse 
C)  $( 8 x + 2 ) ^ { 2 } + ( 8 y + 9 ) ^ { 2 } = 320$ ; circle 
D)  $( x + 2 ) ^ { 2 } + ( y + 9 ) ^ { 2 } = 40$ ; circle 
E)  $( x + 2 ) ^ { 2 } + ( y + 9 ) ^ { 2 } = 20$ ; circle

Question 3

Find the vertices of the conic.  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$

Accepted Answer

A) Vertices: $( 0 , \pm 3 )$ 
B) Vertices: $( \pm 6,0 )$ 
C) Vertices: $( 0 , \pm 6 )$ 
D) Vertices: $( \pm 3,6 )$ 
E) Vertices: $( \pm 3,0 )$ 
A) Vertices: $( 0 , \pm 3 )$ 
B) Vertices: $( \pm 6,0 )$ 
C) Vertices: $( 0 , \pm 6 )$ 
D) Vertices: $( \pm 3,6 )$ 
E) Vertices: $( \pm 3,0 )$

Question 4

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $6 x + 7 y - 13 = 0$

Accepted Answer

A)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
B)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$. 
C)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$.. 
D)  $\theta \approx 2.5536 \text { radians } \approx 146.3 ^ { \circ }$ 
E)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$... 
A)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ 
B)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$. 
C)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$.. 
D)  $\theta \approx 2.5536 \text { radians } \approx 146.3 ^ { \circ }$ 
E)  $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$...

Question 5

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form.  $x y - 6 = 0$

Accepted Answer

A)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 6 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } = 1$ 
B)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 6 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } = 1$ 
C)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 12 } = 1$ 
D)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 12 } = 1$ 
E)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 6 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 12 } = 1$ 
A)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 6 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } = 1$ 
B)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 6 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } = 1$ 
C)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 12 } = 1$ 
D)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 12 } = 1$ 
E)  $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 6 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 12 } = 1$

Question 6

Use the discriminant to classify the graph.  $x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0$

Accepted Answer

A) The graph is a cone. 
B) The graph is a parabola. 
C) The graph is a ellipse or circle. 
D) The graph is a hyperbola. 
E) The graph is a line. 
A) The graph is a cone. 
B) The graph is a parabola. 
C) The graph is a ellipse or circle. 
D) The graph is a hyperbola. 
E) The graph is a line.

Question 7

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $x = t - 1$ $y = 5 t + 1$

Accepted Answer

A)  $y = 5 x - 6$ 
B)  $y = 5 x + 6$ 
C)  $y = x + 5$ 
D)  $y = x + 6$ 
E)  $y = 5 x + 1$ 
A)  $y = 5 x - 6$ 
B)  $y = 5 x + 6$ 
C)  $y = x + 5$ 
D)  $y = x + 6$ 
E)  $y = 5 x + 1$

Question 8

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m.

Accepted Answer

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

Question 9

Select the parametric equations matching with the following graph.

Accepted Answer

A) Serpentine curve: $x = \frac { 1 } { 4 } \cot \Theta , y = 4 \sin \Theta \cos \Theta$ 
B) Serpentine curve: $x = \frac { 1 } { 5 } \tan \Theta , y = 5 \sin \Theta \cos \Theta$ 
C) Serpentine curve: $x = \frac { 1 } { 5 } \cot \Theta , y = 4 \sin \Theta \cos \Theta$ 
D) Serpentine curve: $x = \frac { 1 } { 4 } \cot \Theta , y = 5 \sin \Theta \cos \Theta$ 
E) Serpentine curve: $x = \tan \theta , y = \sin \Theta$ 
A) Serpentine curve: $x = \frac { 1 } { 4 } \cot \Theta , y = 4 \sin \Theta \cos \Theta$ 
B) Serpentine curve: $x = \frac { 1 } { 5 } \tan \Theta , y = 5 \sin \Theta \cos \Theta$ 
C) Serpentine curve: $x = \frac { 1 } { 5 } \cot \Theta , y = 4 \sin \Theta \cos \Theta$ 
D) Serpentine curve: $x = \frac { 1 } { 4 } \cot \Theta , y = 5 \sin \Theta \cos \Theta$ 
E) Serpentine curve: $x = \tan \theta , y = \sin \Theta$

Question 10

Select the graph of $r = 3 \cos \theta$ over the interval.Describe the part of the graph obtained in this case.  $0 \leq \theta \leq \pi$

Accepted Answer

A)   Upper half of circle 
B)   Upper half of circle 
C)    Upper half of circle 
D)    Upper half of circle 
E)   Upper half of circle 
A)   Upper half of circle 
B)   Upper half of circle 
C)    Upper half of circle 
D)    Upper half of circle 
E)   Upper half of circle

Question 11

Convert the rectangular equation to polar form.Assume r > 1.  $y = 2$

Accepted Answer

A)  $r = 2 \cos \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 2 \csc \theta$ 
D)  $r = 2 \sin \theta$ 
E)  $r = 2 \sec \theta$ 
A)  $r = 2 \cos \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 2 \csc \theta$ 
D)  $r = 2 \sin \theta$ 
E)  $r = 2 \sec \theta$

Question 12

Identify the conic by writing the equation in standard form.  $18 y ^ { 2 } - 24 x ^ { 2 } + 216 y + 336 x - 543 = 0$

Accepted Answer

A)  $\frac { ( y - 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse 
B)  $\frac { ( y + 6 ) ^ { 2 } } { \frac { 97 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 97 } { 8 } } = 1$ ; hyperbola 
C)  $\frac { ( y - 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ; hyperbola 
D)  $\frac { ( y + 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ; hyperbola 
E)  $\frac { ( y + 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse 
A)  $\frac { ( y - 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse 
B)  $\frac { ( y + 6 ) ^ { 2 } } { \frac { 97 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 97 } { 8 } } = 1$ ; hyperbola 
C)  $\frac { ( y - 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ; hyperbola 
D)  $\frac { ( y + 6 ) ^ { 2 } } { \frac { 5 } { 6 } } - \frac { ( x - 7 ) ^ { 2 } } { \frac { 5 } { 8 } } = 1$ ; hyperbola 
E)  $\frac { ( y + 6 ) ^ { 2 } } { \frac { 149 } { 5 } } + \frac { ( x - 7 ) ^ { 2 } } { \frac { 149 } { 10 } } = 1$ ; ellipse

Question 13

Find the center, vertices and foci of the hyperbola.  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$

Accepted Answer

A) Center: (0, 0)Vertices: $( 0,6 )$ Foci: $( 0 , \sqrt { 61 } )$ 
B) Center: (0, 0)Vertices: $( \pm 6,0 )$ Foci: $( \pm \sqrt { 61 } , 0 )$ 
C) Center: (0, 0)Vertices: $( \pm 6,0 )$ Foci: $( \sqrt { 61 } , 0 )$ 
D) Center: (0, 0)Vertices: $( 6,0 )$ Foci: $( \pm \sqrt { 61 } , 0 )$ 
E) Center: (0, 0)Vertices: $( 0 , \pm 5 )$ Foci: $( 0 , \pm \sqrt { 61 } )$ 
A) Center: (0, 0)Vertices: $( 0,6 )$ Foci: $( 0 , \sqrt { 61 } )$ 
B) Center: (0, 0)Vertices: $( \pm 6,0 )$ Foci: $( \pm \sqrt { 61 } , 0 )$ 
C) Center: (0, 0)Vertices: $( \pm 6,0 )$ Foci: $( \sqrt { 61 } , 0 )$ 
D) Center: (0, 0)Vertices: $( 6,0 )$ Foci: $( \pm \sqrt { 61 } , 0 )$ 
E) Center: (0, 0)Vertices: $( 0 , \pm 5 )$ Foci: $( 0 , \pm \sqrt { 61 } )$

Question 14

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 
Foci: $( \pm 5,0 )$ ; major axis of length 12

Accepted Answer

A)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 11 } = 1$ 
B)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 5 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 11 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 11 } = 1$ 
A)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 11 } = 1$ 
B)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 5 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 11 } = 1$ 
E)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 11 } = 1$

Question 15

Select the correct graph of the polar equation.Describe your viewing window.  $r = \frac { \pi } { 4 }$

Accepted Answer

A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 2 \
X _ { \max } = 2 \
X _ { s c l } = 0.5 \
Y _ { \min } = - 2 \
Y _ { \max } = 2 \
Y _ { s c l } = 0.5
\end{array}$

Question 16

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.  $100 x ^ { 2 } + 100 y ^ { 2 } - 100 x + 400 y + 403 = 0$

Accepted Answer

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

Question 17

The Halley's Comet has an elliptical orbit with an eccentricity of $e \approx 0.907$ .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Accepted Answer

A)  $\frac { 1.139 } { 1 - \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
B)  $\frac { 1.139 } { 1 + 0.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
C)  $\frac { 1.139 } { 1 + 1.967 \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
D)  $\frac { 1.139 } { 1 - 1.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
E)  $\overline { 1 + 1.139 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
A)  $\frac { 1.139 } { 1 - \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
B)  $\frac { 1.139 } { 1 + 0.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
C)  $\frac { 1.139 } { 1 + 1.967 \cos \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
D)  $\frac { 1.139 } { 1 - 1.967 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit. 
E)  $\overline { 1 + 1.139 \sin \theta }$ Closest point to the sun is $\approx$ 0.579 astronomical unit.

Question 18

Find the vertex, focus, and directrix of the parabola.  $y ^ { 2 } = - 3 x$

Accepted Answer

A) Vertex: (0,0); Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ; Directrix: $x = - \frac { 3 } { 4 }$ 
B) Vertex: (0,0); Focus: $\left( - \frac { 1 } { 3 } , 0 \right)$ ; Directrix: $x = \frac { 1 } { 3 }$ 
C) Vertex: (0,0); Focus: $\left( \frac { 1 } { 3 } , 0 \right)$ ; Directrix: $x = \frac { 1 } { 3 }$ 
D) Vertex: (0,0); Focus: $\left( \frac { 3 } { 4 } , 0 \right)$ ; Directrix: $x = - \frac { 3 } { 4 }$ 
E) Vertex: (0,0); Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ; Directrix: $x = \frac { 3 } { 4 }$ 
A) Vertex: (0,0); Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ; Directrix: $x = - \frac { 3 } { 4 }$ 
B) Vertex: (0,0); Focus: $\left( - \frac { 1 } { 3 } , 0 \right)$ ; Directrix: $x = \frac { 1 } { 3 }$ 
C) Vertex: (0,0); Focus: $\left( \frac { 1 } { 3 } , 0 \right)$ ; Directrix: $x = \frac { 1 } { 3 }$ 
D) Vertex: (0,0); Focus: $\left( \frac { 3 } { 4 } , 0 \right)$ ; Directrix: $x = - \frac { 3 } { 4 }$ 
E) Vertex: (0,0); Focus: $\left( - \frac { 3 } { 4 } , 0 \right)$ ; Directrix: $x = \frac { 3 } { 4 }$

Question 19

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 
Vertical major axis passes through the points $( 0,7 ) \text { and } ( 5,0 )$ .

Accepted Answer

A)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$ 
E)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$

Question 20

Identify the conic and select its correct graph.  $r = \frac { 4 } { 2 + 8 \sin \theta }$

Accepted Answer

A)  $e = 4 > 1 \Rightarrow$ Hyperbola   
B)  $e = 4 > 1 \Rightarrow$ Hyperbola   
C)  $e = 4 > 1 \Rightarrow$ Hyperbola   
D)  $e = 4 > 1 \Rightarrow$ Hyperbola   
E)  $e = 4 > 1 \Rightarrow$ Hyperbola   
A)  $e = 4 > 1 \Rightarrow$ Hyperbola   
B)  $e = 4 > 1 \Rightarrow$ Hyperbola   
C)  $e = 4 > 1 \Rightarrow$ Hyperbola   
D)  $e = 4 > 1 \Rightarrow$ Hyperbola   
E)  $e = 4 > 1 \Rightarrow$ Hyperbola

Identify the conic and select its correct graph. $r = \frac { 3 } { 2 + 6 \sin \theta }$

Identify the conic by writing the equation in standard form. $8 x ^ { 2 } + 8 y ^ { 2 } + 32 x + 144 y + 520 = 0$

Find the vertices of the conic. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $6 x + 7 y - 13 = 0$

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. $x y - 6 = 0$

Use the discriminant to classify the graph. $x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t - 1$ $y = 5 t + 1$

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m.

Select the parametric equations matching with the following graph.

Select the graph of $r = 3 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $0 \leq \theta \leq \pi$

Convert the rectangular equation to polar form.Assume r > 1. $y = 2$

Identify the conic by writing the equation in standard form. $18 y ^ { 2 } - 24 x ^ { 2 } + 216 y + 336 x - 543 = 0$

Find the center, vertices and foci of the hyperbola. $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: $( \pm 5,0 )$ ; major axis of length 12

Select the correct graph of the polar equation.Describe your viewing window. $r = \frac { \pi } { 4 }$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $100 x ^ { 2 } + 100 y ^ { 2 } - 100 x + 400 y + 403 = 0$

The Halley's Comet has an elliptical orbit with an eccentricity of $e \approx 0.907$ .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Find the vertex, focus, and directrix of the parabola. $y ^ { 2 } = - 3 x$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis passes through the points $( 0,7 ) \text { and } ( 5,0 )$ .

Identify the conic and select its correct graph. $r = \frac { 4 } { 2 + 8 \sin \theta }$

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

Identify the conic and select its correct graph. r=32+6sin⁡θr = \frac { 3 } { 2 + 6 \sin \theta }r=2+6sinθ3​

Identify the conic by writing the equation in standard form. 8x2+8y2+32x+144y+520=08 x ^ { 2 } + 8 y ^ { 2 } + 32 x + 144 y + 520 = 08x2+8y2+32x+144y+520=0

Find the vertices of the conic. x29+y236=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 19x2​+36y2​=1

Find the inclination θ\thetaθ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 6x+7y−13=06 x + 7 y - 13 = 06x+7y−13=0

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. xy−6=0x y - 6 = 0xy−6=0

Use the discriminant to classify the graph. x2+xy+10y2+x+y−10=0x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0x2+xy+10y2+x+y−10=0

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=t−1x = t - 1x=t−1 y=5t+1y = 5 t + 1y=5t+1

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m.

Select the parametric equations matching with the following graph.

Select the graph of r=3cos⁡θr = 3 \cos \thetar=3cosθ over the interval.Describe the part of the graph obtained in this case. 0≤θ≤π0 \leq \theta \leq \pi0≤θ≤π

Convert the rectangular equation to polar form.Assume r > 1. y=2y = 2y=2

Identify the conic by writing the equation in standard form. 18y2−24x2+216y+336x−543=018 y ^ { 2 } - 24 x ^ { 2 } + 216 y + 336 x - 543 = 018y2−24x2+216y+336x−543=0

Find the center, vertices and foci of the hyperbola. y225−x236=1\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 125y2​−36x2​=1

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: (±5,0)( \pm 5,0 )(±5,0) ; major axis of length 12

Select the correct graph of the polar equation.Describe your viewing window. r=π4r = \frac { \pi } { 4 }r=4π​

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 100x2+100y2−100x+400y+403=0100 x ^ { 2 } + 100 y ^ { 2 } - 100 x + 400 y + 403 = 0100x2+100y2−100x+400y+403=0

The Halley's Comet has an elliptical orbit with an eccentricity of e≈0.907e \approx 0.907e≈0.907 .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Find the vertex, focus, and directrix of the parabola. y2=−3xy ^ { 2 } = - 3 xy2=−3x

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis passes through the points (0,7) and (5,0)( 0,7 ) \text { and } ( 5,0 )(0,7) and (5,0) .

Identify the conic and select its correct graph. r=42+8sin⁡θr = \frac { 4 } { 2 + 8 \sin \theta }r=2+8sinθ4​

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

Identify the conic and select its correct graph. $r = \frac { 3 } { 2 + 6 \sin \theta }$

Identify the conic by writing the equation in standard form. $8 x ^ { 2 } + 8 y ^ { 2 } + 32 x + 144 y + 520 = 0$

Find the vertices of the conic. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $6 x + 7 y - 13 = 0$

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. $x y - 6 = 0$

Use the discriminant to classify the graph. $x ^ { 2 } + x y + 10 y ^ { 2 } + x + y - 10 = 0$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t - 1$ $y = 5 t + 1$

Select the graph of $r = 3 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $0 \leq \theta \leq \pi$

Convert the rectangular equation to polar form.Assume r > 1. $y = 2$

Identify the conic by writing the equation in standard form. $18 y ^ { 2 } - 24 x ^ { 2 } + 216 y + 336 x - 543 = 0$

Find the center, vertices and foci of the hyperbola. $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 36 } = 1$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: $( \pm 5,0 )$ ; major axis of length 12

Select the correct graph of the polar equation.Describe your viewing window. $r = \frac { \pi } { 4 }$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $100 x ^ { 2 } + 100 y ^ { 2 } - 100 x + 400 y + 403 = 0$

The Halley's Comet has an elliptical orbit with an eccentricity of $e \approx 0.907$ .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun

Find the vertex, focus, and directrix of the parabola. $y ^ { 2 } = - 3 x$

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertical major axis passes through the points $( 0,7 ) \text { and } ( 5,0 )$ .

Identify the conic and select its correct graph. $r = \frac { 4 } { 2 + 8 \sin \theta }$