Question 1

Write Equations of Hyperbolas in Standard Form
-Endpoints of transverse axis: $( 0 , - 6 ) , ( 0,6 )$; asymptote: $\mathrm { y } = \frac { 3 } { 10 } \mathrm { x }$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 400 } = 1$ 
B)  $\frac { y ^ { 2 } } { 400 } - \frac { x ^ { 2 } } { 36 } = 1$ 
C)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$ 
A)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 400 } = 1$ 
B)  $\frac { y ^ { 2 } } { 400 } - \frac { x ^ { 2 } } { 36 } = 1$ 
C)  $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$

Question 2

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$y ^ { 2 } = - 12 x$$

Accepted Answer

A)  focus: $( - 3,0 )$
directrix: $x = 3$ 
B)  focus: $( 0 , - 3 )$
directrix: $y = 3$ 
C)  focus: $( 3,0 )$
directrix: $x = - 3$ 
D)  focus: $( - 3,0 )$  
directrix: $y = 3$ 
A)  focus: $( - 3,0 )$
directrix: $x = 3$ 
B)  focus: $( 0 , - 3 )$
directrix: $y = 3$ 
C)  focus: $( 3,0 )$
directrix: $x = - 3$ 
D)  focus: $( - 3,0 )$  
directrix: $y = 3$

Question 3

Find the standard form of the equation of the ellipse satisfying the given conditions.
-Foci: $( 0 , - 2 ) , ( 0,2 ) ; y$-intercepts: $- 5$ and 5

Accepted Answer

A)  $\frac { x ^ { 2 } } { 21 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 21 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 21 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 21 } + \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 21 } = 1$ 
C)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 21 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$

Question 4

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
x + y = 7
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 4,3 ) , ( 3,4 ) \}$ 
B)  $\{ ( - 4,3 ) , ( - 3,4 ) \}$ 
C)  $\{ ( 4 , - 3 ) , ( 3 , - 4 ) \}$ 
D)  $\{ ( - 4 , - 3 ) , ( - 3 , - 4 ) \}$ 
A)  $\{ ( 4,3 ) , ( 3,4 ) \}$ 
B)  $\{ ( - 4,3 ) , ( - 3,4 ) \}$ 
C)  $\{ ( 4 , - 3 ) , ( 3 , - 4 ) \}$ 
D)  $\{ ( - 4 , - 3 ) , ( - 3 , - 4 ) \}$

Question 5

Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Vertex: $( 4 , - 6 )$; Focus: $( 8 , - 6 )$

Accepted Answer

A)  $( y + 6 ) ^ { 2 } = 16 ( x - 4 )$ 
B)  $( y + 6 ) ^ { 2 } = - 16 ( x - 4 )$ 
C)  $( x + 4 ) ^ { 2 } = - 8 ( y - 6 )$ 
D)  $( x + 4 ) ^ { 2 } = 8 ( y - 6 )$ 
A)  $( y + 6 ) ^ { 2 } = 16 ( x - 4 )$ 
B)  $( y + 6 ) ^ { 2 } = - 16 ( x - 4 )$ 
C)  $( x + 4 ) ^ { 2 } = - 8 ( y - 6 )$ 
D)  $( x + 4 ) ^ { 2 } = 8 ( y - 6 )$

Question 6

Graph Hyperbolas Centered at the Origin
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
-$$36 y ^ { 2 } - 4 x ^ { 2 } = 144$$

Accepted Answer

A)  Asymptotes: $y = \pm \frac { 1 } { 3 } x$
  
B)  Asymptotes: $\mathrm { y } = \pm 3 \mathrm { x }$
  
C)  Asymptotes: $\mathrm { y } = \pm \frac { 1 } { 3 } \mathrm { x }$
  
D)  Asymptotes: $\mathrm { y } = \pm 3 \mathrm { x }$
  
A)  Asymptotes: $y = \pm \frac { 1 } { 3 } x$
  
B)  Asymptotes: $\mathrm { y } = \pm 3 \mathrm { x }$
  
C)  Asymptotes: $\mathrm { y } = \pm \frac { 1 } { 3 } \mathrm { x }$
  
D)  Asymptotes: $\mathrm { y } = \pm 3 \mathrm { x }$

Question 7

Find the foci of the ellipse whose equation is given.
-$$25 ( x + 3 ) ^ { 2 } + 36 ( y + 1 ) ^ { 2 } = 900$$

Accepted Answer

A)  foci at $( - 3 + \sqrt { 11 } , - 1 )$ and $( - 3 - \sqrt { 11 } , - 1 )$ 
B)  foci at $( - 1 + \sqrt { 11 } , - 3 )$ and $( - 1 - \sqrt { 11 } , - 3 )$ 
C)  foci at $( - \sqrt { 11 } , - 1 )$ and $( \sqrt { 11 } , - 1 )$ 
D)  foci at $( - 3 + \sqrt { 11 } , - 3 )$ and $( - 3 - \sqrt { 11 } , - 3 )$ 
A)  foci at $( - 3 + \sqrt { 11 } , - 1 )$ and $( - 3 - \sqrt { 11 } , - 1 )$ 
B)  foci at $( - 1 + \sqrt { 11 } , - 3 )$ and $( - 1 - \sqrt { 11 } , - 3 )$ 
C)  foci at $( - \sqrt { 11 } , - 1 )$ and $( \sqrt { 11 } , - 1 )$ 
D)  foci at $( - 3 + \sqrt { 11 } , - 3 )$ and $( - 3 - \sqrt { 11 } , - 3 )$

Question 8

Find the vertices and locate the foci for the hyperbola whose equation is given.
-$$y = \pm \sqrt { x ^ { 2 } - 6 }$$

Accepted Answer

A)  vertices: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$ 
B)  vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$ 
C)  vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$ 
D)  vertices: $( 0 , - \sqrt { 6 } ) , ( 0 , \sqrt { 6 } )$
foci: $( 0 , - 2 \sqrt { 3 } ) , ( 0,2 \sqrt { 3 } )$ 
A)  vertices: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$ 
B)  vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$ 
C)  vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$ 
D)  vertices: $( 0 , - \sqrt { 6 } ) , ( 0 , \sqrt { 6 } )$
foci: $( 0 , - 2 \sqrt { 3 } ) , ( 0,2 \sqrt { 3 } )$

Question 9

Solve the problem.
-A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 25 feet. If the distance across the top of the mirror is 58 inches, how deep is the mirror in the center?

Accepted Answer

A)  $\frac { 841 } { 1200 } \mathrm { in }$. 
B)  $\frac { 841 } { 100 } \mathrm { in }$. 
C)  $\frac { 841 } { 14400 }$ in. 
D)  $\frac { 625 } { 116 } \mathrm { in }$. 
A)  $\frac { 841 } { 1200 } \mathrm { in }$. 
B)  $\frac { 841 } { 100 } \mathrm { in }$. 
C)  $\frac { 841 } { 14400 }$ in. 
D)  $\frac { 625 } { 116 } \mathrm { in }$.

Question 10

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range.
-$$y = x ^ { 2 } + 8 x + 22$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 11

Find the foci of the ellipse whose equation is given.
-$$\frac { ( x - 3 ) ^ { 2 } } { 36 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

Accepted Answer

A)  foci at $( 3 + 2 \sqrt { 5 } , 1 )$ and $( 3 - 2 \sqrt { 5 } , 1 )$ 
B)  foci at $( 1 + 2 \sqrt { 5 } , 3 )$ and $( 1 - 2 \sqrt { 5 } , 3 )$ 
C)  foci at $( - 2 \sqrt { 5 } , 1 )$ and $( 2 \sqrt { 5 } , 1 )$ 
D)  foci at $( 3 + 2 \sqrt { 5 } , 3 )$ and $( 3 - 2 \sqrt { 5 } , 3 )$ 
A)  foci at $( 3 + 2 \sqrt { 5 } , 1 )$ and $( 3 - 2 \sqrt { 5 } , 1 )$ 
B)  foci at $( 1 + 2 \sqrt { 5 } , 3 )$ and $( 1 - 2 \sqrt { 5 } , 3 )$ 
C)  foci at $( - 2 \sqrt { 5 } , 1 )$ and $( 2 \sqrt { 5 } , 1 )$ 
D)  foci at $( 3 + 2 \sqrt { 5 } , 3 )$ and $( 3 - 2 \sqrt { 5 } , 3 )$

Question 12

Solve Applied Problems Involving Hyperbolas
Solve the problem.
-A satellite following the hyperbolic path shown in the picture turns rapidly at $( 0,3 )$ and then moves closer and closer to the line $\mathrm { y } = \frac { 5 } { 2 } \mathrm { x }$ as it gets farther from the tracking station at the origin. Find the equation that describes the path of the satellite if the center of the hyperbola is at $( 0,0 )$.

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { \frac { 36 } { 25 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { \left( \frac { 75 } { 6 } \right) ^ { 2 } } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 36 } { 25 } } - \frac { x ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { \left( \frac { 75 } { 6 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { \frac { 36 } { 25 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { \left( \frac { 75 } { 6 } \right) ^ { 2 } } = 1$ 
C)  $\frac { y ^ { 2 } } { \frac { 36 } { 25 } } - \frac { x ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { \left( \frac { 75 } { 6 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 9 } = 1$

Question 13

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$x ^ { 2 } = 40 y$$

Accepted Answer

A)  focus: $( 0,10 )$
directrix: $y = - 10$ 
B)  focus: $( 10,0 )$
directrix: $y = 10$ 
C)  focus: $( 10,0 )$
directrix: $x = 10$ 
D)  focus: $( 0 , - 10 )$
directrix: $\mathrm { x } = - 10$ 
A)  focus: $( 0,10 )$
directrix: $y = - 10$ 
B)  focus: $( 10,0 )$
directrix: $y = 10$ 
C)  focus: $( 10,0 )$
directrix: $x = 10$ 
D)  focus: $( 0 , - 10 )$
directrix: $\mathrm { x } = - 10$

Question 14

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$x = 6 y ^ { 2 }$$

Accepted Answer

A)  focus: $\left( \frac { 1 } { 24 } , 0 \right)$
directrix: $x = - \frac { 1 } { 24 }$ 
B)  focus: $\left( 0 , \frac { 1 } { 24 } \right)$
 directrix: $\mathrm { y } = - \frac { 1 } { 24 }$ 
C)  focus: $\left( \frac { 1 } { 6 } , 0 \right)$
directrix: $x = - \frac { 1 } { 6 }$ 
D)  focus: $\left( \frac { 1 } { 24 } , 0 \right)$
 directrix: $x = \frac { 1 } { 24 }$ 
A)  focus: $\left( \frac { 1 } { 24 } , 0 \right)$
directrix: $x = - \frac { 1 } { 24 }$ 
B)  focus: $\left( 0 , \frac { 1 } { 24 } \right)$
 directrix: $\mathrm { y } = - \frac { 1 } { 24 }$ 
C)  focus: $\left( \frac { 1 } { 6 } , 0 \right)$
directrix: $x = - \frac { 1 } { 6 }$ 
D)  focus: $\left( \frac { 1 } { 24 } , 0 \right)$
 directrix: $x = \frac { 1 } { 24 }$

Question 15

Solve the problem.
-A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 170 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Accepted Answer

A) 29.1 ft 
B) 0.2 ft 
C) 3.7 ft 
D) 21.3 ft 
A) 29.1 ft 
B) 0.2 ft 
C) 3.7 ft 
D) 21.3 ft

Question 16

Use the center, vertices, and asymptotes to graph the hyperbola.
-$$\frac { ( x + 1 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

Accepted Answer

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

Question 17

Graph Hyperbolas Not Centered at the Origin
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
-$$\frac { ( y - 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 100 } = 1$$

Accepted Answer

A)  Center: $( 2,1 )$; Vertices: $( 2 , - 2 )$ and $( 2,4 )$; Foci: $( 2,1 - \sqrt { 109 } )$ and $( 2,1 + \sqrt { 109 } )$ 
B)  Center: $( - 2 , - 1 )$; Vertices: $( - 2 , - 4 )$ and $( - 2,2 )$; Foci: $( - 2 , - 1 - \sqrt { 109 } )$ and $( - 2 , - 1 + \sqrt { 109 } )$ 
C)  Center: $( 2,1 )$; Vertices: $( 2,1 - \sqrt { 109 } )$ and $( 2,1 + \sqrt { 109 } )$; Foci: $( 2 , - 2 )$ and $( 2,4 )$ 
D)  Center: $( 2,1 )$; Vertices: $( 2 , - 1 )$ and $( 3,5 )$; Foci: $( 2,2 - \sqrt { 109 } )$ and $( 3,2 + \sqrt { 109 } )$ 
A)  Center: $( 2,1 )$; Vertices: $( 2 , - 2 )$ and $( 2,4 )$; Foci: $( 2,1 - \sqrt { 109 } )$ and $( 2,1 + \sqrt { 109 } )$ 
B)  Center: $( - 2 , - 1 )$; Vertices: $( - 2 , - 4 )$ and $( - 2,2 )$; Foci: $( - 2 , - 1 - \sqrt { 109 } )$ and $( - 2 , - 1 + \sqrt { 109 } )$ 
C)  Center: $( 2,1 )$; Vertices: $( 2,1 - \sqrt { 109 } )$ and $( 2,1 + \sqrt { 109 } )$; Foci: $( 2 , - 2 )$ and $( 2,4 )$ 
D)  Center: $( 2,1 )$; Vertices: $( 2 , - 1 )$ and $( 3,5 )$; Foci: $( 2,2 - \sqrt { 109 } )$ and $( 3,2 + \sqrt { 109 } )$

Question 18

Solve Applied Problems Involving Ellipses
Solve the problem.
-The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 30 feet and the height of the arch over the center of the roadway is 13 feet. Two trucks plan to
Use this road. They are both 10 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an
Overall height of 13 feet. Draw a rough sketch of the situation and determine which of the trucks can pass
Under the bridge.

Accepted Answer

A) Truck 1 can pass under the bridge, but Truck 2 cannot. 
B) Both Truck 1 and Truck 2 can pass under the bridge. 
C) Neither Truck 1 nor Truck 2 can pass under the bridge. 
D) Truck 2 can pass under the bridge, but Truck 1 cannot. 
A) Truck 1 can pass under the bridge, but Truck 2 cannot. 
B) Both Truck 1 and Truck 2 can pass under the bridge. 
C) Neither Truck 1 nor Truck 2 can pass under the bridge. 
D) Truck 2 can pass under the bridge, but Truck 1 cannot.

Question 19

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
25 x ^ { 2 } + 16 y ^ { 2 } = 400
\end{array} \right.$$

Accepted Answer

A)  $\{ ( 0,5 ) , ( 0 , - 5 ) \}$ 
B)  $\{ ( 5,0 ) , ( - 5,0 ) \}$ 
C)  $\{ ( 0,4 ) , ( 0 , - 4 ) \}$ 
D)  $\{ ( 4,0 ) , ( - 4,0 ) \}$ 
A)  $\{ ( 0,5 ) , ( 0 , - 5 ) \}$ 
B)  $\{ ( 5,0 ) , ( - 5,0 ) \}$ 
C)  $\{ ( 0,4 ) , ( 0 , - 4 ) \}$ 
D)  $\{ ( 4,0 ) , ( - 4,0 ) \}$

Question 20

Graph Hyperbolas Centered at the Origin
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
-$$\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  Asymptotes: $y = \pm \frac { 3 } { 5 } x$
  
B)  Asymptotes: $y = \pm \frac { 5 } { 3 } x$
  
C)  Asymptotes: $\mathrm { y } = \pm \frac { 3 } { 5 } \mathrm { x }$
  
D)  Asymptotes: $y = \pm \frac { 5 } { 3 } x$
  
A)  Asymptotes: $y = \pm \frac { 3 } { 5 } x$
  
B)  Asymptotes: $y = \pm \frac { 5 } { 3 } x$
  
C)  Asymptotes: $\mathrm { y } = \pm \frac { 3 } { 5 } \mathrm { x }$
  
D)  Asymptotes: $y = \pm \frac { 5 } { 3 } x$

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: $( 0 , - 6 ) , ( 0,6 )$ ; asymptote: $\mathrm { y } = \frac { 3 } { 10 } \mathrm { x }$

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - $y ^ { 2 } = - 12 x$

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: $( 0 , - 2 ) , ( 0,2 ) ; y$ -intercepts: $- 5$ and 5

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Vertex: $( 4 , - 6 )$ ; Focus: $( 8 , - 6 )$

Find the foci of the ellipse whose equation is given. - $25 ( x + 3 ) ^ { 2 } + 36 ( y + 1 ) ^ { 2 } = 900$

Find the vertices and locate the foci for the hyperbola whose equation is given. - $y = \pm \sqrt { x ^ { 2 } - 6 }$

Solve the problem. -A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 25 feet. If the distance across the top of the mirror is 58 inches, how deep is the mirror in the center?

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - $y = x ^ { 2 } + 8 x + 22$

Find the foci of the ellipse whose equation is given. - $\frac { ( x - 3 ) ^ { 2 } } { 36 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - $x ^ { 2 } = 40 y$

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - $x = 6 y ^ { 2 }$

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 170 feet and a maximum height of 30 feet. Find the height of the arch at 15 feet from its center.

Use the center, vertices, and asymptotes to graph the hyperbola. - $\frac { ( x + 1 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$ $Use the center, vertices, and asymptotes to graph the hyperbola. - \frac { ( x + 1 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - $\frac { ( y - 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 100 } = 1$

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Exam 7: Conic Sections

Write Equations of Hyperbolas in Standard Form -Endpoints of transverse axis: (0,−6),(0,6)( 0 , - 6 ) , ( 0,6 )(0,−6),(0,6) ; asymptote: y=310x\mathrm { y } = \frac { 3 } { 10 } \mathrm { x }y=103​x

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - y2=−12xy ^ { 2 } = - 12 xy2=−12x

Find the standard form of the equation of the ellipse satisfying the given conditions. -Foci: (0,−2),(0,2);y( 0 , - 2 ) , ( 0,2 ) ; y(0,−2),(0,2);y -intercepts: −5- 5−5 and 5

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. - {x2+y2=25x+y=7\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = 7\end{array} \right.{x2+y2=25x+y=7​

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Vertex: (4,−6)( 4 , - 6 )(4,−6) ; Focus: (8,−6)( 8 , - 6 )(8,−6)

Graph Hyperbolas Centered at the Origin Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes. - 36y2−4x2=14436 y ^ { 2 } - 4 x ^ { 2 } = 14436y2−4x2=144

Find the foci of the ellipse whose equation is given. - 25(x+3)2+36(y+1)2=90025 ( x + 3 ) ^ { 2 } + 36 ( y + 1 ) ^ { 2 } = 90025(x+3)2+36(y+1)2=900

Find the vertices and locate the foci for the hyperbola whose equation is given. - y=±x2−6y = \pm \sqrt { x ^ { 2 } - 6 }y=±x2−6​