Question 1

Give the standard form of the equation of the parabola with the given characteristics.

Accepted Answer

A)  $( y - 8 ) ^ { 2 } = 8 ( x + 6 )$ 
B)  $( y + 8 ) ^ { 2 } = - 8 ( x - 6 )$ 
C)  $( x - 6 ) ^ { 2 } = 8 ( y + 8 )$ 
D)  $( y - 8 ) ^ { 2 } = - 8 ( x + 6 )$ 
E)  $( x + 6 ) ^ { 2 } = 8 ( y - 8 )$ 
A)  $( y - 8 ) ^ { 2 } = 8 ( x + 6 )$ 
B)  $( y + 8 ) ^ { 2 } = - 8 ( x - 6 )$ 
C)  $( x - 6 ) ^ { 2 } = 8 ( y + 8 )$ 
D)  $( y - 8 ) ^ { 2 } = - 8 ( x + 6 )$ 
E)  $( x + 6 ) ^ { 2 } = 8 ( y - 8 )$

Question 2

Identify the conic as a circle or an ellipse then find the radius. $$\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 1$$

Accepted Answer

A)  Ellipse
Center: 1 
B)  Circle
Radius: $\frac { 2 } { 3 }$ 
C)  Circle
Radius: 1 
D)  Ellipse
Center: $\frac { 2 } { 3 }$ 
E)  None of the above 
A)  Ellipse
Center: 1 
B)  Circle
Radius: $\frac { 2 } { 3 }$ 
C)  Circle
Radius: 1 
D)  Ellipse
Center: $\frac { 2 } { 3 }$ 
E)  None of the above

Question 3

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. $\text { Vertices: } ( \pm 4,0 ) ; \text { asymptotes: } y = \pm 6 x$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 576 } = 1$ 
B)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 576 } = 1$ 
C)  $\frac { y ^ { 2 } } { 576 } - \frac { x ^ { 2 } } { 16 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 576 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 576 } = 1$ 
A)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 576 } = 1$ 
B)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 576 } = 1$ 
C)  $\frac { y ^ { 2 } } { 576 } - \frac { x ^ { 2 } } { 16 } = 1$ 
D)  $\frac { y ^ { 2 } } { 16 } + \frac { x ^ { 2 } } { 576 } = 1$ 
E)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 576 } = 1$

Question 4

Select the graph for following equation. $$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$$

Accepted Answer

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

Question 5

Using following result find a set of parametric equation of the line. $$x = x _ { 1 } + t \left( x _ { 2 } - x _ { 1 } \right) , y = y _ { 1 } + t \left( y _ { 2 } - y _ { 1 } \right)$$
Line: passes through $( 0,0 )$ and $( 6,4 )$

Accepted Answer

A)  $x = - 6 t , y = 4 t$ 
B)  $x = 4 t , y = 6 t$ 
C)  $x = 6 t , y = - 4 t$ 
D)  $x = 6 t , y = 4 t$ 
E)  $x = - 4 t , y = - 6 t$ 
A)  $x = - 6 t , y = 4 t$ 
B)  $x = 4 t , y = 6 t$ 
C)  $x = 6 t , y = - 4 t$ 
D)  $x = 6 t , y = 4 t$ 
E)  $x = - 4 t , y = - 6 t$

Question 6

Select the graph of the following equation $x ^ { 2 } = 2 y$

Accepted Answer

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

Question 7

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.  $r ^ { 2 } = 9 \sin \theta$

Accepted Answer

A)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
B)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
C) 
$\begin{array} { l } 
r = 3 \sqrt { \sin \theta } \
r = - 3 \sqrt { \sin \theta } \
0 \leq \theta \leq \pi
\end{array}$
  
D)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
E)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
A)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
B)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
C) 
$\begin{array} { l } 
r = 3 \sqrt { \sin \theta } \
r = - 3 \sqrt { \sin \theta } \
0 \leq \theta \leq \pi
\end{array}$
  
D)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$
  
E)  $r = 3 \sqrt { \sin \theta }$
$r = - 3 \sqrt { \sin \theta }$
$0 \leq \theta \leq \pi$

Question 8

Convert the polar equation to rectangular form. $r ^ { 2 } = 2 \sin \theta$

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 2 } y ^ { 2 / 3 } = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 2 } y ^ { 2 / 3 } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
E)  $x ^ { 2 } - y ^ { 2 } - \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 2 } y ^ { 2 / 3 } = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 2 } y ^ { 2 / 3 } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$ 
E)  $x ^ { 2 } - y ^ { 2 } - \sqrt [ 3 ] { 4 } y ^ { 2 / 3 } = 0$

Question 9

Find a polar equation of the conic with its focus at the pole.

Accepted Answer

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

Question 10

Find the standard form of the equation of the ellipse with the given characteristics.

Accepted Answer

A) 
$\frac { x + 6 ^ { 2 } } { 81 } + \frac { y + 2 ^ { 2 } } { 77 } = 1$ 
B) 
$\frac { x + 2 ^ { 2 } } { 77 } + \frac { y + 6 ^ { 2 } } { 81 } = 1$ 
C) 
$\frac { x - 2 ^ { 2 } } { 77 } + \frac { y - 6 ^ { 2 } } { 81 } = 1$ 
D) 
$\frac { x - 2 ^ { 2 } } { 81 } + \frac { y - 6 ^ { 2 } } { 77 } = 1$ 
E) 
$\frac { x - 6 ^ { 2 } } { 81 } + \frac { y - 2 ^ { 2 } } { 77 } = 1$ 
A) 
$\frac { x + 6 ^ { 2 } } { 81 } + \frac { y + 2 ^ { 2 } } { 77 } = 1$ 
B) 
$\frac { x + 2 ^ { 2 } } { 77 } + \frac { y + 6 ^ { 2 } } { 81 } = 1$ 
C) 
$\frac { x - 2 ^ { 2 } } { 77 } + \frac { y - 6 ^ { 2 } } { 81 } = 1$ 
D) 
$\frac { x - 2 ^ { 2 } } { 81 } + \frac { y - 6 ^ { 2 } } { 77 } = 1$ 
E) 
$\frac { x - 6 ^ { 2 } } { 81 } + \frac { y - 2 ^ { 2 } } { 77 } = 1$

Question 11

Consider a line with slope m and y-intercept $( 0,6 )$ Write the distance d between the point $( 5,1 )$ and the line as a function of m.

Accepted Answer

A)  $\frac { 5 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
B)  $\frac { 5 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$ 
C)  $\frac { 5 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
D)  $\frac { 5 | m + 5 | } { \sqrt { m ^ { 2 } + 1 } }$ 
E)  $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
A)  $\frac { 5 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
B)  $\frac { 5 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$ 
C)  $\frac { 5 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$ 
D)  $\frac { 5 | m + 5 | } { \sqrt { m ^ { 2 } + 1 } }$ 
E)  $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$

Question 12

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. $\text { Directrix: } y = 3$

Accepted Answer

A)  $y ^ { 2 } = - 12 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$ 
A)  $y ^ { 2 } = - 12 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = 12 x$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $x ^ { 2 } = - 12 y$

Question 13

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

Accepted Answer

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

Question 14

Find the inclination $\theta$ (in degrees) of the line with a slope of $m$ . Round your answer to one decimal places. $m = - \frac { 5 } { 2 }$

Accepted Answer

A)  $\theta \approx 110.8 ^ { \circ }$ 
B)  $\theta \approx 112.8 ^ { \circ }$ 
C)  $\theta \approx 111.8 ^ { \circ }$ 
D)  $\theta \approx 109.8 ^ { \circ }$ 
E)  $\theta \approx 113.8 ^ { \circ }$ 
A)  $\theta \approx 110.8 ^ { \circ }$ 
B)  $\theta \approx 112.8 ^ { \circ }$ 
C)  $\theta \approx 111.8 ^ { \circ }$ 
D)  $\theta \approx 109.8 ^ { \circ }$ 
E)  $\theta \approx 113.8 ^ { \circ }$

Question 15

Select the polar equation with graph.

Accepted Answer

A)  $\frac { 4 } { 1 + 3 \cos \theta }$ 
B)  $\frac { 4 } { 1 + 3 \sin \theta }$ 
C)  $\frac { 1 } { 1 - 3 \sin \theta }$ 
D)  $\frac { 4 } { 1 - 3 \sin \theta }$ 
E)  $\frac { 4 } { 1 - 3 \cos \theta }$ 
A)  $\frac { 4 } { 1 + 3 \cos \theta }$ 
B)  $\frac { 4 } { 1 + 3 \sin \theta }$ 
C)  $\frac { 1 } { 1 - 3 \sin \theta }$ 
D)  $\frac { 4 } { 1 - 3 \sin \theta }$ 
E)  $\frac { 4 } { 1 - 3 \cos \theta }$

Question 16

Select the graph of the following equation $x ^ { 2 } = 2 y$

Accepted Answer

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

Question 17

Identify the conic and select its correct graph. $$r = \frac { 2 } { 2 - 4 \cos \theta }$$

Accepted Answer

A)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
B)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
C)  $e=2>1 \Rightarrow \text { Hyperbola }$
  
D)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
E)  $e = 2 > 1 \Rightarrow$ Hyperbola
  
A)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
B)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
C)  $e=2>1 \Rightarrow \text { Hyperbola }$
  
D)  $\quad e = 2 > 1 \Rightarrow$ Hyperbola
  
E)  $e = 2 > 1 \Rightarrow$ Hyperbola

Question 18

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. 
$\begin{array} { l } 
x = t + 5 \
y = t ^ { 2 }
\end{array}$

Accepted Answer

A)  $y = t - 5$ 
B)  $y = x ^ { 2 } + 10 x + 25$ 
C)  $y = x ^ { 2 }$ 
D)  $y = x ^ { 2 } - 10 x + 25$ 
E)  $y = t + 5$ 
A)  $y = t - 5$ 
B)  $y = x ^ { 2 } + 10 x + 25$ 
C)  $y = x ^ { 2 }$ 
D)  $y = x ^ { 2 } - 10 x + 25$ 
E)  $y = t + 5$

Question 19

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$21 x ^ { 2 } - 13 x - 230 y - 115 = 0$$

Accepted Answer

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

Question 20

Select the correct equation of the following graph.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 25 } = 1$ 
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 0$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$ 
E)  $\frac { y ^ { 2 } } { 4 } + \frac { x ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 25 } = 1$ 
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 0$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$ 
E)  $\frac { y ^ { 2 } } { 4 } + \frac { x ^ { 2 } } { 25 } = 1$

Give the standard form of the equation of the parabola with the given characteristics.

Identify the conic as a circle or an ellipse then find the radius. $\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 1$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. $\text { Vertices: } ( \pm 4,0 ) ; \text { asymptotes: } y = \pm 6 x$

Select the graph for following equation. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Using following result find a set of parametric equation of the line. $x = x _ { 1 } + t \left( x _ { 2 } - x _ { 1 } \right) , y = y _ { 1 } + t \left( y _ { 2 } - y _ { 1 } \right)$ Line: passes through $( 0,0 )$ and $( 6,4 )$

Select the graph of the following equation $x ^ { 2 } = 2 y$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r ^ { 2 } = 9 \sin \theta$

Convert the polar equation to rectangular form. $r ^ { 2 } = 2 \sin \theta$

Find a polar equation of the conic with its focus at the pole.

Find the standard form of the equation of the ellipse with the given characteristics.

Consider a line with slope m and y-intercept $( 0,6 )$ Write the distance d between the point $( 5,1 )$ and the line as a function of m.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. $\text { Directrix: } y = 3$

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

Find the inclination $\theta$ (in degrees) of the line with a slope of $m$ . Round your answer to one decimal places. $m = - \frac { 5 } { 2 }$

Select the polar equation with graph.

Select the graph of the following equation $x ^ { 2 } = 2 y$

Identify the conic and select its correct graph. $r = \frac { 2 } { 2 - 4 \cos \theta }$

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

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $21 x ^ { 2 } - 13 x - 230 y - 115 = 0$

Select the correct equation of the following graph.

Functions and Their Graphs

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Exam 6: Topics in Analytic Geometry

Give the standard form of the equation of the parabola with the given characteristics.

Identify the conic as a circle or an ellipse then find the radius. x24/9+(y+1)24/9=1\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 14/9x2​+4/9(y+1)2​=1

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (±4,0); asymptotes: y=±6x\text { Vertices: } ( \pm 4,0 ) ; \text { asymptotes: } y = \pm 6 x Vertices: (±4,0); asymptotes: y=±6x

Select the graph for following equation. x29+y24=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 19x2​+4y2​=1

Select the graph of the following equation x2=2yx ^ { 2 } = 2 yx2=2y

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r2=9sin⁡θr ^ { 2 } = 9 \sin \thetar2=9sinθ

Convert the polar equation to rectangular form. r2=2sin⁡θr ^ { 2 } = 2 \sin \thetar2=2sinθ

Find a polar equation of the conic with its focus at the pole.

Find the standard form of the equation of the ellipse with the given characteristics.

Consider a line with slope m and y-intercept (0,6)( 0,6 )(0,6) Write the distance d between the point (5,1)( 5,1 )(5,1) and the line as a function of m.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Directrix: y=3\text { Directrix: } y = 3 Directrix: y=3

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

Find the inclination θ\thetaθ (in degrees) of the line with a slope of mmm . Round your answer to one decimal places. m=−52m = - \frac { 5 } { 2 }m=−25​

Select the polar equation with graph.

Select the graph of the following equation x2=2yx ^ { 2 } = 2 yx2=2y

Identify the conic and select its correct graph. r=22−4cos⁡θr = \frac { 2 } { 2 - 4 \cos \theta }r=2−4cosθ2​

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

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 21x2−13x−230y−115=021 x ^ { 2 } - 13 x - 230 y - 115 = 021x2−13x−230y−115=0

Select the correct equation of the following graph.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

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Identify the conic as a circle or an ellipse then find the radius. $\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 1$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. $\text { Vertices: } ( \pm 4,0 ) ; \text { asymptotes: } y = \pm 6 x$

Select the graph for following equation. $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Select the graph of the following equation $x ^ { 2 } = 2 y$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r ^ { 2 } = 9 \sin \theta$

Convert the polar equation to rectangular form. $r ^ { 2 } = 2 \sin \theta$

Consider a line with slope m and y-intercept $( 0,6 )$ Write the distance d between the point $( 5,1 )$ and the line as a function of m.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. $\text { Directrix: } y = 3$

Find the inclination $\theta$ (in degrees) of the line with a slope of $m$ . Round your answer to one decimal places. $m = - \frac { 5 } { 2 }$

Select the graph of the following equation $x ^ { 2 } = 2 y$

Identify the conic and select its correct graph. $r = \frac { 2 } { 2 - 4 \cos \theta }$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $21 x ^ { 2 } - 13 x - 230 y - 115 = 0$