Question 1

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m. ​

Accepted Answer

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

Question 2

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $x = \cos \theta$ $y = 5 \sin 2 \theta$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $y = \pm 10 x \sqrt { 1 + x ^ { 2 } }$ 
C)  $y = \pm 10 x \sqrt { 1 + x }$ 
D) $\frac { x ^ { 2 } } { 1 } - \frac { y ^ { 2 } } { 5 } = 1$ 
E)  $y = \pm 10 x \sqrt { 1 - x ^ { 2 } }$ 
A)  $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $y = \pm 10 x \sqrt { 1 + x ^ { 2 } }$ 
C)  $y = \pm 10 x \sqrt { 1 + x }$ 
D) $\frac { x ^ { 2 } } { 1 } - \frac { y ^ { 2 } } { 5 } = 1$ 
E)  $y = \pm 10 x \sqrt { 1 - x ^ { 2 } }$

Question 3

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $x = t + 8$ $y = \frac { t } { t + 8 }$

Accepted Answer

A)  $y = \frac { x - 8 } { 9 x }$ 
B)  $y = \frac { x } { x - 8 }$ 
C)  $y = x - 8$ 
D)  $y = \frac { x - 8 } { x }$ 
E)  $y = x + 8$ 
A)  $y = \frac { x - 8 } { 9 x }$ 
B)  $y = \frac { x } { x - 8 }$ 
C)  $y = x - 8$ 
D)  $y = \frac { x - 8 } { x }$ 
E)  $y = x + 8$

Question 4

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.    $$a = 3 , b = \frac { 3 \pi } { 2 }$$

Accepted Answer

A) Rectangular coordinates: (0,3) 
B) Rectangular coordinates: (-3,0) 
C) Rectangular coordinates: (3,0) 
D) Rectangular coordinates: (0,-3) 
E) Rectangular coordinates: (3,3) 
A) Rectangular coordinates: (0,3) 
B) Rectangular coordinates: (-3,0) 
C) Rectangular coordinates: (3,0) 
D) Rectangular coordinates: (0,-3) 
E) Rectangular coordinates: (3,3)

Question 5

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$

Accepted Answer

A) center: (8, 6) vertices: (-8, -6), (8, 6) 
B) center: (0, 0) vertices: (0, -8), (0, 8) 
C) center: (0, 0) vertices: (-8, 0), (8, 0) 
D) center: (8, 0) vertices: (0, -6), (0, 6) 
E) center: (0, 0) vertices: (-6, 0), (6, 0) 
A) center: (8, 6) vertices: (-8, -6), (8, 6) 
B) center: (0, 0) vertices: (0, -8), (0, 8) 
C) center: (0, 0) vertices: (-8, 0), (8, 0) 
D) center: (8, 0) vertices: (0, -6), (0, 6) 
E) center: (0, 0) vertices: (-6, 0), (6, 0)

Question 6

Select the correct graph of the polar equation.Describe your viewing window.  $r = 2 \csc \theta + 5$

Accepted Answer

A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
A)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
B)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
C)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
D)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$ 
E)    $\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 12 \
X _ { \max } = 12 \
X _ { s c l } = 2 \
Y _ { \min } = - 12 \
Y _ { \max } = 12 \
Y _ { s c l } = 2
\end{array}$

Question 7

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points.
 $r = 1$

Accepted Answer

A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
A) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
B) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
C) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
D) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$    
E) Symmetric with respect to $\theta = \frac { \pi } { 2 }$ , polar axis, poleCircle with radius $r = 1$

Question 8

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( - 5.7 , - 0.8 )$

Accepted Answer

A) Rectangular coordinates: (-3.97,5.09) 
B) Rectangular coordinates: (-2.97,5.09) 
C) Rectangular coordinates: (-3.97,4.09) 
D) Rectangular coordinates: (-2.97,4.09) 
E) Rectangular coordinates: (4.09,-3.97) 
A) Rectangular coordinates: (-3.97,5.09) 
B) Rectangular coordinates: (-2.97,5.09) 
C) Rectangular coordinates: (-3.97,4.09) 
D) Rectangular coordinates: (-2.97,4.09) 
E) Rectangular coordinates: (4.09,-3.97)

Question 9

Sketch the graph of the ellipse, using the latera recta.  $9 x ^ { 2 } + 4 y ^ { 2 } = 36$

Accepted Answer

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

Question 10

Find the vertex and focus of the parabola for the given equation and select its graph.  $y = - 3 x ^ { 2 }$

Accepted Answer

A) Vertex: (0,0)Focus: (0,3)   
B) Vertex: (0,0)Focus: (0,-12)   
C) Vertex: (0,0)Focus: (0,-3)   
D) Vertex: (0,0)Focus: $\left( 0 , - \frac { 1 } { 12 } \right)$   
E) Vertex: (0,0)Focus: $\left( 0 , \frac { 1 } { 3 } \right)$   
A) Vertex: (0,0)Focus: (0,3)   
B) Vertex: (0,0)Focus: (0,-12)   
C) Vertex: (0,0)Focus: (0,-3)   
D) Vertex: (0,0)Focus: $\left( 0 , - \frac { 1 } { 12 } \right)$   
E) Vertex: (0,0)Focus: $\left( 0 , \frac { 1 } { 3 } \right)$

Question 11

Identify the conic by writing the equation in standard form.  $4 x ^ { 2 } + 9 y ^ { 2 } + 40 x + 54 y + 145 = 0$

Accepted Answer

A)  $\frac { ( x + 5 ) ^ { 2 } } { 9 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ ; ellipse 
B)  $( 3 x + 5 ) ^ { 2 } + ( 2 y + 1 ) ^ { 2 } = 167$ ; circle 
C)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 422 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 211 } { 2 } } = 1$ ; ellipse 
D)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 73 } { 3 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 219 } { 4 } } = 1$ ; ellipse 
E)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 167 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 167 } { 4 } } = 1$ ; ellipse 
A)  $\frac { ( x + 5 ) ^ { 2 } } { 9 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ ; ellipse 
B)  $( 3 x + 5 ) ^ { 2 } + ( 2 y + 1 ) ^ { 2 } = 167$ ; circle 
C)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 422 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 211 } { 2 } } = 1$ ; ellipse 
D)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 73 } { 3 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 219 } { 4 } } = 1$ ; ellipse 
E)  $\frac { ( x + 5 ) ^ { 2 } } { \frac { 167 } { 9 } } + \frac { ( y + 3 ) ^ { 2 } } { \frac { 167 } { 4 } } = 1$ ; ellipse

Question 12

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. 
Parabola: $y ^ { 2 } - 24 x = 0$ Tangent Line: $x - y + 6 = 0$

Accepted Answer

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

Question 13

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. 
Vertices: (0,±5); focies: (0,±6)

Accepted Answer

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

Question 14

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

Accepted Answer

A)  $x ^ { 2 } = \frac { 5 } { 2 } y$ ; Focus: $\left( 0 , \frac { 5 } { 8 } \right)$ 
B)  $y ^ { 2 } = - \frac { 5 } { 2 } x$ ; Focus: $\left( - \frac { 5 } { 8 } , 0 \right)$ 
C)  $x ^ { 2 } = - \frac { 5 } { 2 } y$ ; Focus: $\left( 0 , - \frac { 5 } { 8 } \right)$ 
D)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ; Focus: $\left( \frac { 5 } { 8 } , 0 \right)$ 
E)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ; Focus: $( 5,0 )$ 
A)  $x ^ { 2 } = \frac { 5 } { 2 } y$ ; Focus: $\left( 0 , \frac { 5 } { 8 } \right)$ 
B)  $y ^ { 2 } = - \frac { 5 } { 2 } x$ ; Focus: $\left( - \frac { 5 } { 8 } , 0 \right)$ 
C)  $x ^ { 2 } = - \frac { 5 } { 2 } y$ ; Focus: $\left( 0 , - \frac { 5 } { 8 } \right)$ 
D)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ; Focus: $\left( \frac { 5 } { 8 } , 0 \right)$ 
E)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ; Focus: $( 5,0 )$

Question 15

Find the distance between the point and the line.  Point Line
$( 4,5 ) \quad x + 2 = 0$

Accepted Answer

A)  $d = 8$ 
B)  $d = 9$ 
C)  $d = 6$ 
D)  $d = 10$ 
E)  $d = 7$ 
A)  $d = 8$ 
B)  $d = 9$ 
C)  $d = 6$ 
D)  $d = 10$ 
E)  $d = 7$

Question 16

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

Accepted Answer

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

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = \cos \theta$ $y = 5 \sin 2 \theta$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t + 8$ $y = \frac { t } { t + 8 }$

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 3 , b = \frac { 3 \pi } { 2 }$ $a = 3 , b = \frac { 3 \pi } { 2 }$

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$

Select the correct graph of the polar equation.Describe your viewing window. $r = 2 \csc \theta + 5$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 1$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( - 5.7 , - 0.8 )$

Sketch the graph of the ellipse, using the latera recta. $9 x ^ { 2 } + 4 y ^ { 2 } = 36$

Find the vertex and focus of the parabola for the given equation and select its graph. $y = - 3 x ^ { 2 }$

Identify the conic by writing the equation in standard form. $4 x ^ { 2 } + 9 y ^ { 2 } + 40 x + 54 y + 145 = 0$

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: $y ^ { 2 } - 24 x = 0$ Tangent Line: $x - y + 6 = 0$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±5); focies: (0,±6)

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the distance between the point and the line. Point Line $( 4,5 ) \quad x + 2 = 0$

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

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

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Exam 10: Topics In Analytic Geometry

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m. ​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=cos⁡θx = \cos \thetax=cosθ y=5sin⁡2θy = 5 \sin 2 \thetay=5sin2θ

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=t+8x = t + 8x=t+8 y=tt+8y = \frac { t } { t + 8 }y=t+8t​

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a=3,b=3π2a = 3 , b = \frac { 3 \pi } { 2 }a=3,b=23π​

Find the center and vertices of the ellipse. x264+y236=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 164x2​+36y2​=1

Select the correct graph of the polar equation.Describe your viewing window. r=2csc⁡θ+5r = 2 \csc \theta + 5r=2cscθ+5

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. r=1r = 1r=1

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. (−5.7,−0.8)( - 5.7 , - 0.8 )(−5.7,−0.8)

Sketch the graph of the ellipse, using the latera recta. 9x2+4y2=369 x ^ { 2 } + 4 y ^ { 2 } = 369x2+4y2=36

Find the vertex and focus of the parabola for the given equation and select its graph. y=−3x2y = - 3 x ^ { 2 }y=−3x2

Identify the conic by writing the equation in standard form. 4x2+9y2+40x+54y+145=04 x ^ { 2 } + 9 y ^ { 2 } + 40 x + 54 y + 145 = 04x2+9y2+40x+54y+145=0

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: y2−24x=0y ^ { 2 } - 24 x = 0y2−24x=0 Tangent Line: x−y+6=0x - y + 6 = 0x−y+6=0

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±5); focies: (0,±6)

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the distance between the point and the line. Point Line (4,5)x+2=0( 4,5 ) \quad x + 2 = 0(4,5)x+2=0

Find the vertices and asymptotes of the hyperbola. 9y2−16x2=1449 y ^ { 2 } - 16 x ^ { 2 } = 1449y2−16x2=144

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

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1) and the line as a function of m.

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = \cos \theta$ $y = 5 \sin 2 \theta$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = t + 8$ $y = \frac { t } { t + 8 }$

A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b) shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 3 , b = \frac { 3 \pi } { 2 }$ $a = 3 , b = \frac { 3 \pi } { 2 }$

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$

Select the correct graph of the polar equation.Describe your viewing window. $r = 2 \csc \theta + 5$

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $r = 1$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( - 5.7 , - 0.8 )$

Sketch the graph of the ellipse, using the latera recta. $9 x ^ { 2 } + 4 y ^ { 2 } = 36$

Find the vertex and focus of the parabola for the given equation and select its graph. $y = - 3 x ^ { 2 }$

Identify the conic by writing the equation in standard form. $4 x ^ { 2 } + 9 y ^ { 2 } + 40 x + 54 y + 145 = 0$

The equations of a parabola and a tangent line to the parabola are given.Select the correct graph of both equations in the same viewing window. Parabola: $y ^ { 2 } - 24 x = 0$ Tangent Line: $x - y + 6 = 0$

Find the distance between the point and the line. Point Line $( 4,5 ) \quad x + 2 = 0$

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