Question 1

Convert the equation to the standard form for an ellipse by completing the square on x and y.
-$$25 x ^ { 2 } + 36 y ^ { 2 } - 50 x - 216 y - 551 = 0$$

Accepted Answer

A)  $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 3 ) ^ { 2 } } { 36 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$ 
A)  $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x - 3 ) ^ { 2 } } { 36 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$

Question 2

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.
-$$\begin{aligned}
16 x ^ { 2 } + y ^ { 2 } & = 16 \
y ^ { 2 } - 16 x ^ { 2 } & = 16
\end{aligned}$$

Accepted Answer

A)  $\{ ( 0 , - 4 ) , ( 0,4 ) \}$ 
B)  $\{ ( 0 , - 4 ) \}$ 
C)  $\{ ( 0,16 ) \}$ 
D)  $\{ ( 4,0 ) , ( 4,0 ) \}$ 
A)  $\{ ( 0 , - 4 ) , ( 0,4 ) \}$ 
B)  $\{ ( 0 , - 4 ) \}$ 
C)  $\{ ( 0,16 ) \}$ 
D)  $\{ ( 4,0 ) , ( 4,0 ) \}$

Question 3

Find the vertices and locate the foci for the hyperbola whose equation is given.
-$$16 x ^ { 2 } - 4 y ^ { 2 } = 64$$

Accepted Answer

A)  vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$ 
B)  vertices: $( 0 , - 2 ) , ( 0,2 )$
foci: $( 0 , - 2 \sqrt { 5 } ) , ( 0,2 \sqrt { 5 } )$ 
C)  vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$ 
D)  vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$ 
A)  vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$ 
B)  vertices: $( 0 , - 2 ) , ( 0,2 )$
foci: $( 0 , - 2 \sqrt { 5 } ) , ( 0,2 \sqrt { 5 } )$ 
C)  vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$ 
D)  vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$

Question 4

Additional Concepts
Determine the direction in which the parabola opens, and the vertex.
-$$y ^ { 2 } - 4 y - x - 1 = 0$$

Accepted Answer

A)  Opens to the right; $( - 5,2 )$ 
B)  Opens to the left; $( 5 , - 2 )$ 
C)  Opens downward; $( 2,5 )$ 
D)  Opens downward; $( - 2,5 )$ 
A)  Opens to the right; $( - 5,2 )$ 
B)  Opens to the left; $( 5 , - 2 )$ 
C)  Opens downward; $( 2,5 )$ 
D)  Opens downward; $( - 2,5 )$

Question 5

Graph the semi-ellipse.
-$$y = - \sqrt { 16 - 9 x ^ { 2 } }$$

Accepted Answer

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

Question 6

Find the standard form of the equation of the hyperbola.
-

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$

Question 7

Graph the ellipse and locate the foci.
-$$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  
foci at $( 2 \sqrt { 14 } , 0 )$ and $( - 2 \sqrt { 14 } , 0 )$
  
B)  foci at $( 0,2 \sqrt { 14 } )$ and $( 0 , - 2 \sqrt { 14 } )$
  
C)  foci at $( 5 \sqrt { 3 } , 0 )$ and $( - 5 \sqrt { 3 } , 0 )$
  
D)  foci at $( 0,5 \sqrt { 3 } )$ and $( 0 , - 5 \sqrt { 3 } )$
  
A)  
foci at $( 2 \sqrt { 14 } , 0 )$ and $( - 2 \sqrt { 14 } , 0 )$
  
B)  foci at $( 0,2 \sqrt { 14 } )$ and $( 0 , - 2 \sqrt { 14 } )$
  
C)  foci at $( 5 \sqrt { 3 } , 0 )$ and $( - 5 \sqrt { 3 } , 0 )$
  
D)  foci at $( 0,5 \sqrt { 3 } )$ and $( 0 , - 5 \sqrt { 3 } )$

Question 8

Graph Hyperbolas Not Centered at the Origin
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
-$$( y - 1 ) ^ { 2 } - 4 ( x - 3 ) ^ { 2 } = 4$$

Accepted Answer

A)  Center: $( 3,1 )$; Vertices: $( 3 , - 1 )$ and $( 3,3 )$; Foci: $( 3,1 - \sqrt { 5 } )$ and $( 3,1 + \sqrt { 5 } )$ 
B)  Center: $( - 3 , - 1 )$; Vertices: $( - 3 , - 3 )$ and $( - 3,1 )$; Foci: $( - 3 , - 1 - \sqrt { 5 } )$ and $( - 3 , - 1 + \sqrt { 5 } )$ 
C)  Center: $( 3,1 )$; Vertices: $( - 3 , - 2 )$ and $( 3,2 ) ;$ Foci: $( 3 , - \sqrt { 5 } )$ and $( 3 , \sqrt { 5 } )$ 
D)  Center: $( 3,1 )$; Vertices: $( 4,0 )$ and $( 4,4 )$; Foci: $( 4,2 - \sqrt { 5 } )$ and $( 4,2 + \sqrt { 5 } )$ 
A)  Center: $( 3,1 )$; Vertices: $( 3 , - 1 )$ and $( 3,3 )$; Foci: $( 3,1 - \sqrt { 5 } )$ and $( 3,1 + \sqrt { 5 } )$ 
B)  Center: $( - 3 , - 1 )$; Vertices: $( - 3 , - 3 )$ and $( - 3,1 )$; Foci: $( - 3 , - 1 - \sqrt { 5 } )$ and $( - 3 , - 1 + \sqrt { 5 } )$ 
C)  Center: $( 3,1 )$; Vertices: $( - 3 , - 2 )$ and $( 3,2 ) ;$ Foci: $( 3 , - \sqrt { 5 } )$ and $( 3 , \sqrt { 5 } )$ 
D)  Center: $( 3,1 )$; Vertices: $( 4,0 )$ and $( 4,4 )$; Foci: $( 4,2 - \sqrt { 5 } )$ and $( 4,2 + \sqrt { 5 } )$

Question 9

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range.
-$y ^ { 2 } - 12 y - x + 38 = 0$

Accepted Answer

A)  Domain: $( 2 , \infty ]$
Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , - 2 )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 2 ]$ 
A)  Domain: $( 2 , \infty ]$
Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , - 2 )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 2 ]$

Question 10

Solve the problem.
-A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface of the dish and are reflected to the focus, where the receiver is located. The satellite dish shown has a diameter of 10 feet and a depth of 7 feet. The parabola is positioned in a rectangular coordinate system with its vertex at the origin. The receiver should be placed at the focus $( 0 , \mathrm { p } )$. The value of $\mathrm { p }$ is given by the equation $\mathrm { a } = \frac { 1 } { 4 \mathrm { p } }$. How far from the base of the dish should the receiver be placed?

Accepted Answer

A)  $\frac { 25 } { 28 }$ feet from the base 
B)  $3 \frac { 4 } { 7 }$ feet from the base 
C)  $\frac { 7 } { 25 }$ feet from the base 
D)  $1 \frac { 3 } { 25 }$ feet from the base 
A)  $\frac { 25 } { 28 }$ feet from the base 
B)  $3 \frac { 4 } { 7 }$ feet from the base 
C)  $\frac { 7 } { 25 }$ feet from the base 
D)  $1 \frac { 3 } { 25 }$ feet from the base

Question 11

Solve the problem.
-An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers
Stand 40 inches apart. At a point between the towers and 10 inches along the road from the base of one
Tower, the cable is 1 inches above the roadway. Find the height of the towers.

Accepted Answer

A) 4 in. 
B) 4.5 in. 
C) 3.5 in. 
D) 6 in. 
A) 4 in. 
B) 4.5 in. 
C) 3.5 in. 
D) 6 in.

Question 12

Graph the parabola.
-$y^{2}=20 x$

Accepted Answer

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

Question 13

Find the vertices and locate the foci for the hyperbola whose equation is given.
-$\frac { \mathrm { x } ^ { 2 } } { 144 } - \frac { \mathrm { y } ^ { 2 } } { 4 } = 1$

Accepted Answer

A)  vertices: $( - 12,0 ) , ( 12,0 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$ 
B)  vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$ 
C)  vertices: $( 0 , - 12 ) , ( 0,12 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$ 
D)  vertices: $( - 12,0 ) , ( 12,0 )$
foci: $( - 2,0 ) , ( 2,0 )$ 
A)  vertices: $( - 12,0 ) , ( 12,0 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$ 
B)  vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$ 
C)  vertices: $( 0 , - 12 ) , ( 0,12 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$ 
D)  vertices: $( - 12,0 ) , ( 12,0 )$
foci: $( - 2,0 ) , ( 2,0 )$

Question 14

Graph Parabolas with Vertices Not at the Origin
Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y - 2 ) ^ { 2 } = - 6 ( x - 1 )$$

Accepted Answer

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

Question 15

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$x ^ { 2 } = 11 y$$

Accepted Answer

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

Question 16

Graph Parabolas with Vertices Not at the Origin
Find the vertex, focus, and directrix of the parabola with the given equation.
-$( x - 1 ) ^ { 2 } = 4 ( y + 4 )$

Accepted Answer

A)  vertex: $( 1 , - 4 )$
focus: $( 1 , - 3 )$
directrix: $y = - 5$ 
B)  vertex: $( - 1,4 )$
focus: $( - 1,5 )$
directrix: $y = 3 \quad$ 
C)  vertex: $( - 4,1 )$
focus: $( - 4,2 )$
 directrix: $y = 0$ 
D)  vertex: $( 1 , - 4 )$
focus: $( 1 , - 5 )$
directrix: $x = - 3$ 
A)  vertex: $( 1 , - 4 )$
focus: $( 1 , - 3 )$
directrix: $y = - 5$ 
B)  vertex: $( - 1,4 )$
focus: $( - 1,5 )$
directrix: $y = 3 \quad$ 
C)  vertex: $( - 4,1 )$
focus: $( - 4,2 )$
 directrix: $y = 0$ 
D)  vertex: $( 1 , - 4 )$
focus: $( 1 , - 5 )$
directrix: $x = - 3$

Question 17

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.
-$$\begin{aligned}
( y - 4 ) ^ { 2 } & = x + 16 \
y & = - \frac { 1 } { 4 } x
\end{aligned}$$

Accepted Answer

A)  $\{ ( - 16,4 ) , ( 0,0 ) \}$ 
B)  $\{ ( 16 , - 4 ) , ( 0,0 ) \}$ 
C)  $\{ ( - 16,0 ) , ( 4,0 ) \}$ 
D)  $\{ ( - 16,4 ) \}$ 
A)  $\{ ( - 16,4 ) , ( 0,0 ) \}$ 
B)  $\{ ( 16 , - 4 ) , ( 0,0 ) \}$ 
C)  $\{ ( - 16,0 ) , ( 4,0 ) \}$ 
D)  $\{ ( - 16,4 ) \}$

Question 18

Solve Applied Problems Involving Hyperbolas
Solve the problem.
-Two LORAN stations are positioned 278 miles apart along a straight shore. A ship records a time difference of 0.00086 seconds between the LORAN signals. (The radio signals travel at 186,000 miles per
Second.)Where will the ship reach shore if it were to follow the hyperbola corresponding to this time
Difference? If the ship is 200 miles offshore, what is the position of the ship?

Accepted Answer

A) 59 miles from the master station, (161.9, 200) 
B) 80 miles from the master station, (200, 161.9) 
C) 59 miles from the master station, (200, 161.9) 
D) 80 miles from the master station, (161.9, 200) 
A) 59 miles from the master station, (161.9, 200) 
B) 80 miles from the master station, (200, 161.9) 
C) 59 miles from the master station, (200, 161.9) 
D) 80 miles from the master station, (161.9, 200)

Question 19

Graph Hyperbolas Not Centered at the Origin
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
-$$( x + 4 ) ^ { 2 } - 4 ( y - 4 ) ^ { 2 } = 4$$

Accepted Answer

A)  Center: $( - 4,4 )$; Vertices: $( - 6,4 )$ and $( - 2,4 )$; Foci: $( - 4 - \sqrt { 5 } , 4 )$ and $( - 4 + \sqrt { 5 } , 4 )$ 
B)  Center: $( 4 , - 4 )$; Vertices: $( 2 , - 4 )$ and $( 6 , - 4 )$; Foci: $( 4 - \sqrt { 5 } , 4 )$ and $( 4 + \sqrt { 5 } , 4 )$ 
C)  Center: $( - 4,4 )$; Vertices: $( - 5,5 )$ and $( - 1,5 )$; Foci: $( - 3 - \sqrt { 5 } , 5 )$ and $( - 3 + \sqrt { 5 } , 5 )$ 
D)  Center: $( - 4,4 )$; Vertices: $( 2,4 )$ and $( - 2,4 )$; Foci: $( - \sqrt { 5 } , 4 )$ and $( \sqrt { 5 } , 4 )$ 
A)  Center: $( - 4,4 )$; Vertices: $( - 6,4 )$ and $( - 2,4 )$; Foci: $( - 4 - \sqrt { 5 } , 4 )$ and $( - 4 + \sqrt { 5 } , 4 )$ 
B)  Center: $( 4 , - 4 )$; Vertices: $( 2 , - 4 )$ and $( 6 , - 4 )$; Foci: $( 4 - \sqrt { 5 } , 4 )$ and $( 4 + \sqrt { 5 } , 4 )$ 
C)  Center: $( - 4,4 )$; Vertices: $( - 5,5 )$ and $( - 1,5 )$; Foci: $( - 3 - \sqrt { 5 } , 5 )$ and $( - 3 + \sqrt { 5 } , 5 )$ 
D)  Center: $( - 4,4 )$; Vertices: $( 2,4 )$ and $( - 2,4 )$; Foci: $( - \sqrt { 5 } , 4 )$ and $( \sqrt { 5 } , 4 )$

Question 20

Use the center, vertices, and asymptotes to graph the hyperbola.
-$$\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$$

Accepted Answer

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

Convert the equation to the standard form for an ellipse by completing the square on x and y. - $25 x ^ { 2 } + 36 y ^ { 2 } - 50 x - 216 y - 551 = 0$

Find the vertices and locate the foci for the hyperbola whose equation is given. - $16 x ^ { 2 } - 4 y ^ { 2 } = 64$

Additional Concepts Determine the direction in which the parabola opens, and the vertex. - $y ^ { 2 } - 4 y - x - 1 = 0$

Graph the semi-ellipse. - $y = - \sqrt { 16 - 9 x ^ { 2 } }$ $Graph the semi-ellipse. - y = - \sqrt { 16 - 9 x ^ { 2 } }$

Find the standard form of the equation of the hyperbola. -

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - $( y - 1 ) ^ { 2 } - 4 ( x - 3 ) ^ { 2 } = 4$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - $y ^ { 2 } - 12 y - x + 38 = 0$

Graph the parabola. - $y^{2}=20 x$ $Graph the parabola. - y^{2}=20 x$

Find the vertices and locate the foci for the hyperbola whose equation is given. - $\frac { \mathrm { x } ^ { 2 } } { 144 } - \frac { \mathrm { y } ^ { 2 } } { 4 } = 1$

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - $x ^ { 2 } = 11 y$

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - $( x - 1 ) ^ { 2 } = 4 ( y + 4 )$

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - $( x + 4 ) ^ { 2 } - 4 ( y - 4 ) ^ { 2 } = 4$

Use the center, vertices, and asymptotes to graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$ $Use the center, vertices, and asymptotes to graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$

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Exam 7: Conic Sections

Convert the equation to the standard form for an ellipse by completing the square on x and y. - 25x2+36y2−50x−216y−551=025 x ^ { 2 } + 36 y ^ { 2 } - 50 x - 216 y - 551 = 025x2+36y2−50x−216y−551=0

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. - 16+ =16 -16 =16

Find the vertices and locate the foci for the hyperbola whose equation is given. - 16x2−4y2=6416 x ^ { 2 } - 4 y ^ { 2 } = 6416x2−4y2=64

Additional Concepts Determine the direction in which the parabola opens, and the vertex. - y2−4y−x−1=0y ^ { 2 } - 4 y - x - 1 = 0y2−4y−x−1=0

Graph the semi-ellipse. - y=−16−9x2y = - \sqrt { 16 - 9 x ^ { 2 } }y=−16−9x2​

Find the standard form of the equation of the hyperbola. -

Graph the ellipse and locate the foci. - x281+y225=1\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 181x2​+25y2​=1

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - (y−1)2−4(x−3)2=4( y - 1 ) ^ { 2 } - 4 ( x - 3 ) ^ { 2 } = 4(y−1)2−4(x−3)2=4

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - y2−12y−x+38=0y ^ { 2 } - 12 y - x + 38 = 0y2−12y−x+38=0

Graph the parabola. - y2=20xy^{2}=20 xy2=20x

Find the vertices and locate the foci for the hyperbola whose equation is given. - x2144−y24=1\frac { \mathrm { x } ^ { 2 } } { 144 } - \frac { \mathrm { y } ^ { 2 } } { 4 } = 1144x2​−4y2​=1

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - (y−2)2=−6(x−1)( y - 2 ) ^ { 2 } = - 6 ( x - 1 )(y−2)2=−6(x−1)

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - x2=11yx ^ { 2 } = 11 yx2=11y

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - (x−1)2=4(y+4)( x - 1 ) ^ { 2 } = 4 ( y + 4 )(x−1)2=4(y+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. - (y-4 =x+16 y =-x

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - (x+4)2−4(y−4)2=4( x + 4 ) ^ { 2 } - 4 ( y - 4 ) ^ { 2 } = 4(x+4)2−4(y−4)2=4

Use the center, vertices, and asymptotes to graph the hyperbola. - (y+2)29−(x−2)24=1\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 19(y+2)2​−4(x−2)2​=1

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Convert the equation to the standard form for an ellipse by completing the square on x and y. - $25 x ^ { 2 } + 36 y ^ { 2 } - 50 x - 216 y - 551 = 0$

Find the vertices and locate the foci for the hyperbola whose equation is given. - $16 x ^ { 2 } - 4 y ^ { 2 } = 64$

Additional Concepts Determine the direction in which the parabola opens, and the vertex. - $y ^ { 2 } - 4 y - x - 1 = 0$

Graph the semi-ellipse. - $y = - \sqrt { 16 - 9 x ^ { 2 } }$ $Graph the semi-ellipse. - y = - \sqrt { 16 - 9 x ^ { 2 } }$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - $( y - 1 ) ^ { 2 } - 4 ( x - 3 ) ^ { 2 } = 4$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - $y ^ { 2 } - 12 y - x + 38 = 0$

Graph the parabola. - $y^{2}=20 x$ $Graph the parabola. - y^{2}=20 x$

Find the vertices and locate the foci for the hyperbola whose equation is given. - $\frac { \mathrm { x } ^ { 2 } } { 144 } - \frac { \mathrm { y } ^ { 2 } } { 4 } = 1$

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - $x ^ { 2 } = 11 y$

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - $( x - 1 ) ^ { 2 } = 4 ( y + 4 )$

Graph Hyperbolas Not Centered at the Origin Find the location of the center, vertices, and foci for the hyperbola described by the equation. - $( x + 4 ) ^ { 2 } - 4 ( y - 4 ) ^ { 2 } = 4$

Use the center, vertices, and asymptotes to graph the hyperbola. - $\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$ $Use the center, vertices, and asymptotes to graph the hyperbola. - \frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$