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Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7,-9) directrix: x=−9x = - 9


A) (x−7) 2=−8(y−9) ( x - 7 ) ^ { 2 } = - 8 ( y - 9 )
B) (y−9) 2=−8(x−7) ( y - 9 ) ^ { 2 } = - 8 ( x - 7 )
C) (y+9) 2=8(x+7) ( y + 9 ) ^ { 2 } = 8 ( x + 7 )
D) (y−9) 2=8(x−7) ( y - 9 ) ^ { 2 } = 8 ( x - 7 )
E) (x+7) 2=−8(y+9) ( x + 7 ) ^ { 2 } = - 8 ( y + 9 )

F) A) and E)
G) None of the above

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Give the coordinates of the circle's center and its radius.​ x2+y2−64=0x ^ { 2 } + y ^ { 2 } - 64 = 0 ​


A) (1,1) ;r = 64
B) (0,0) ;r = 8
C) (1,1) ;r = 8
D) (0,0) ;r = 64
E) none of these

F) B) and E)
G) B) and D)

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Find the vertex and directrix of the parabola. x2−18x−12y+33=0x ^ { 2 } - 18 x - 12 y + 33 = 0


A) vertex: (−9,4) ( - 9,4 ) directrix: y=1
B) vertex: (−9,4) ( - 9,4 ) directrix: y=12
C) vertex: (−9,4) ( - 9,4 ) directrix: y=6
D) vertex: (9,−4) ( 9 , - 4 ) directrix: y=-1
E) vertex: (9,−4) ( 9 , - 4 ) directrix: y=-7

F) A) and D)
G) A) and E)

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Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ x29−y225=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1 ​


A) Center: (0,0) Vertices: (-5,0) Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1 ​ A) Center: (0,0) Vertices: (-5,0) B) Center: (0,0) Vertices: (-3,0) C) Center: (0,0) Vertices: (3,0) D) Center: (0,0) Vertices: (±5,0) E) Center: (0,0) Vertices: (±3,0)
B) Center: (0,0) Vertices: (-3,0) Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1 ​ A) Center: (0,0) Vertices: (-5,0) B) Center: (0,0) Vertices: (-3,0) C) Center: (0,0) Vertices: (3,0) D) Center: (0,0) Vertices: (±5,0) E) Center: (0,0) Vertices: (±3,0)
C) Center: (0,0) Vertices: (3,0) Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1 ​ A) Center: (0,0) Vertices: (-5,0) B) Center: (0,0) Vertices: (-3,0) C) Center: (0,0) Vertices: (3,0) D) Center: (0,0) Vertices: (±5,0) E) Center: (0,0) Vertices: (±3,0)
D) Center: (0,0) Vertices: (±5,0) Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1 ​ A) Center: (0,0) Vertices: (-5,0) B) Center: (0,0) Vertices: (-3,0) C) Center: (0,0) Vertices: (3,0) D) Center: (0,0) Vertices: (±5,0) E) Center: (0,0) Vertices: (±3,0)
E) Center: (0,0) Vertices: (±3,0) Find the center and vertices of the hyperbola and sketch its graph,using asymptotes as sketching aids.​ \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1 ​ A) Center: (0,0) Vertices: (-5,0) B) Center: (0,0) Vertices: (-3,0) C) Center: (0,0) Vertices: (3,0) D) Center: (0,0) Vertices: (±5,0) E) Center: (0,0) Vertices: (±3,0)

F) All of the above
G) B) and C)

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E

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (−3,0) ( - 3,0 )


A) x2=yx ^ { 2 } = y
B) y2=12xy ^ { 2 } = 12 x
C) y2=−12xy ^ { 2 } = - 12 x
D) x2=12yx ^ { 2 } = 12 y
E) x2=−12yx ^ { 2 } = - 12 y

F) A) and E)
G) None of the above

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Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7,-2) focus: (-5,-2)


A) (y−2) 2=8(x−7) ( y - 2 ) ^ { 2 } = 8 ( x - 7 )
B) (y+2) 2=8(x+7) ( y + 2 ) ^ { 2 } = 8 ( x + 7 )
C) (y+2) 2=−8(x+7) ( y + 2 ) ^ { 2 } = - 8 ( x + 7 )
D) (x+7) 2=−8(y+2) ( x + 7 ) ^ { 2 } = - 8 ( y + 2 )
E) (x−7) 2=−8(y−2) ( x - 7 ) ^ { 2 } = - 8 ( y - 2 )

F) All of the above
G) A) and D)

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Find the vertex,focus,and directrix of the parabola.​ y=−3x2y = - 3 x ^ { 2 } ​


A) Vertex: (0,0) ;Focus: (0,−112) \left( 0 , - \frac { 1 } { 12 } \right) ;Directrix: y=−112y = - \frac { 1 } { 12 }
B) Vertex:(0,0) ;Focus: (0,−112) \left( 0 , - \frac { 1 } { 12 } \right) ;Directrix: y=112y = \frac { 1 } { 12 }
C) Vertex: (0,0) ;Focus: (0,13) \left( 0 , \frac { 1 } { 3 } \right) ;Directrix: y=13y = \frac { 1 } { 3 }
D) Vertex: (0,0) ;Focus: (0,112) \left( 0 , \frac { 1 } { 12 } \right) ;Directrix: y=112y = \frac { 1 } { 12 }
E) Vertex: (0,0) ;Focus: (0,−13) \left( 0 , - \frac { 1 } { 3 } \right) ;Directrix: y=13y = \frac { 1 } { 3 }

F) All of the above
G) A) and E)

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Find the vertex and focus of the parabola from the given equation and select its graph.​ y=16x2y = \frac { 1 } { 6 } x ^ { 2 } ​


A) Vertex: (0,0) Focus: (0,-1.5) Find the vertex and focus of the parabola from the given equation and select its graph.​ y = \frac { 1 } { 6 } x ^ { 2 } ​ A) Vertex: (0,0) Focus: (0,-1.5) ​ B) Vertex: (0,0) Focus: (-1.5,0) C) Vertex: (0,0) Focus: (0,1.5) D) Vertex: (0,0) Focus: (0,1.5) E) Vertex: (0,0) Focus: (0,-1.5) ​
B) Vertex: (0,0) Focus: (-1.5,0) Find the vertex and focus of the parabola from the given equation and select its graph.​ y = \frac { 1 } { 6 } x ^ { 2 } ​ A) Vertex: (0,0) Focus: (0,-1.5) ​ B) Vertex: (0,0) Focus: (-1.5,0) C) Vertex: (0,0) Focus: (0,1.5) D) Vertex: (0,0) Focus: (0,1.5) E) Vertex: (0,0) Focus: (0,-1.5)
C) Vertex: (0,0) Focus: (0,1.5) Find the vertex and focus of the parabola from the given equation and select its graph.​ y = \frac { 1 } { 6 } x ^ { 2 } ​ A) Vertex: (0,0) Focus: (0,-1.5) ​ B) Vertex: (0,0) Focus: (-1.5,0) C) Vertex: (0,0) Focus: (0,1.5) D) Vertex: (0,0) Focus: (0,1.5) E) Vertex: (0,0) Focus: (0,-1.5)
D) Vertex: (0,0) Focus: (0,1.5) Find the vertex and focus of the parabola from the given equation and select its graph.​ y = \frac { 1 } { 6 } x ^ { 2 } ​ A) Vertex: (0,0) Focus: (0,-1.5) ​ B) Vertex: (0,0) Focus: (-1.5,0) C) Vertex: (0,0) Focus: (0,1.5) D) Vertex: (0,0) Focus: (0,1.5) E) Vertex: (0,0) Focus: (0,-1.5)
E) Vertex: (0,0) Focus: (0,-1.5) Find the vertex and focus of the parabola from the given equation and select its graph.​ y = \frac { 1 } { 6 } x ^ { 2 } ​ A) Vertex: (0,0) Focus: (0,-1.5) ​ B) Vertex: (0,0) Focus: (-1.5,0) C) Vertex: (0,0) Focus: (0,1.5) D) Vertex: (0,0) Focus: (0,1.5) E) Vertex: (0,0) Focus: (0,-1.5)

F) A) and B)
G) A) and C)

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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: x2+20y=0x ^ { 2 } + 20 y = 0 Tangent Line: x+y−5=0x + y - 5 = 0 ​


A) ​ 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: x ^ { 2 } + 20 y = 0 Tangent Line: x + y - 5 = 0 ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ 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: x ^ { 2 } + 20 y = 0 Tangent Line: x + y - 5 = 0 ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ 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: x ^ { 2 } + 20 y = 0 Tangent Line: x + y - 5 = 0 ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ 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: x ^ { 2 } + 20 y = 0 Tangent Line: x + y - 5 = 0 ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ 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: x ^ { 2 } + 20 y = 0 Tangent Line: x + y - 5 = 0 ​ A) ​ B) ​ C) ​ D) ​ E) ​

F) A) and D)
G) C) and D)

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Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Horizontal axis and passes through the point (−4,7) ( - 4,7 ) ​


A) x2=−449yx ^ { 2 } = \frac { - 4 } { 49 } y
B) y2=−449xy ^ { 2 } = \frac { - 4 } { 49 } x
C) y2=49−4xy ^ { 2 } = \frac { 49 } { - 4 } x
D) x2=49−4yx ^ { 2 } = \frac { 49 } { - 4 } y
E) y2=xy ^ { 2 } = x

F) A) and E)
G) B) and E)

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Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Focies: (±7,0) ;major axis of length 16 ​


A) x264+y215=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = 1
B) x264−y215=1\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 15 } = 1
C) −x215+y264=1- \frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1
D) x264+y215=−1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 15 } = - 1
E) x215+y264=1\frac { x ^ { 2 } } { 15 } + \frac { y ^ { 2 } } { 64 } = 1

F) A) and E)
G) B) and C)

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Find the equation of the parabola so that its graph matches the description.​ (y+2) 2=3(x−7) ( y + 2 ) ^ { 2 } = 3 ( x - 7 ) ;lower half of parabola ​


A) y=−2+3(x−7) y = - 2 + \sqrt { 3 ( x - 7 ) }
B) y=−2−3(x−7) y = - 2 - \sqrt { 3 ( x - 7 ) }
C) x=−2+3(y−7) x = - 2 + \sqrt { 3 ( y - 7 ) }
D) x=−2−3(y−7) x = - 2 - \sqrt { 3 ( y - 7 ) }
E) x=−2+3(y+7) x = - 2 + \sqrt { 3 ( y + 7 ) }

F) A) and D)
G) C) and D)

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B

Find the standard form of the equation of the hyperbola with the given characteristics. focies: (±4,0) ,asymptotes: y=±5xy = \pm 5 x


A) x2126−y2126=1\frac { x ^ { 2 } } { \frac { 1 } { 26 } } - \frac { y ^ { 2 } } { \frac { 1 } { 26 } } = 1
B) x2813−y220013=1\frac { x ^ { 2 } } { \frac { 8 } { 13 } } - \frac { y ^ { 2 } } { \frac { 200 } { 13 } } = 1
C) y225−x216=1\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 16 } = 1
D) x216−y2400=1\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 400 } = 1
E) x220013−y2813=1\frac { x ^ { 2 } } { \frac { 200 } { 13 } } - \frac { y ^ { 2 } } { \frac { 8 } { 13 } } = 1

F) A) and B)
G) None of the above

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Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Horizontal axis and passes through the point (3,−2) ( 3 , - 2 ) ​


A) y2=xy ^ { 2 } = x
B) y2=43xy ^ { 2 } = \frac { 4 } { 3 } x
C) y2=34xy ^ { 2 } = \frac { 3 } { 4 } x
D) x2=43yx ^ { 2 } = \frac { 4 } { 3 } y
E) x2=34yx ^ { 2 } = \frac { 3 } { 4 } y

F) None of the above
G) A) and B)

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Find the equation of the parabola so that its graph matches the description.​ (y−5) 2=2(x+1) ( y - 5 ) ^ { 2 } = 2 ( x + 1 ) ;upper half of parabola ​


A) x=2(y+1) +5x = \sqrt { 2 ( y + 1 ) } + 5
B) x=−2(y+1) +5x = - \sqrt { 2 ( y + 1 ) } + 5
C) y=2(x−1) +5y = \sqrt { 2 ( x - 1 ) } + 5
D) y=2(x+1) +5y = \sqrt { 2 ( x + 1 ) } + 5
E) y=−2(x+1) +5y = - \sqrt { 2 ( x + 1 ) } + 5

F) C) and D)
G) B) and E)

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Select the graph of the following equation: ​​ y2=−2xy ^ { 2 } = - 2 x


A) ​ Select the graph of the following equation: ​​ y ^ { 2 } = - 2 x A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ Select the graph of the following equation: ​​ y ^ { 2 } = - 2 x A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ Select the graph of the following equation: ​​ y ^ { 2 } = - 2 x A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ Select the graph of the following equation: ​​ y ^ { 2 } = - 2 x A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ Select the graph of the following equation: ​​ y ^ { 2 } = - 2 x A) ​ B) ​ C) ​ D) ​ E) ​

F) A) and E)
G) C) and E)

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Find the vertex,focus,and directrix of the parabola.​ (x+72) 2=4(y−1) \left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 ) ​


A) Vertex: (−72,1) \left( - \frac { 7 } { 2 } , 1 \right) ;Focus: (−72,2) \left( - \frac { 7 } { 2 } , 2 \right) ;Directrix: y=0y = 0
B) Vertex: (−72,2) \left( - \frac { 7 } { 2 } , 2 \right) ;Focus: (−72,2) \left( - \frac { 7 } { 2 } , 2 \right) ;Directrix: y=1y = 1
C) Vertex: (−72,2) \left( - \frac { 7 } { 2 } , 2 \right) ;Focus: (−72,1) \left( - \frac { 7 } { 2 } , 1 \right) ;Directrix: y=0y = 0
D) Vertex: (−72,1) \left( - \frac { 7 } { 2 } , 1 \right) ;Focus: (−72,2) \left( - \frac { 7 } { 2 } , 2 \right) ;Directrix: y=1y = 1
E) Vertex: (−72,1) \left( - \frac { 7 } { 2 } , 1 \right) ;Focus: (−72,1) \left( - \frac { 7 } { 2 } , 1 \right) ;Directrix: y=1y = 1

F) A) and E)
G) A) and D)

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Find the vertex,focus,and directrix of the parabola.​ y2=10xy ^ { 2 } = 10 x ​


A) Vertex: (0,0) ;Focus: (104,0) \left( \frac { 10 } { 4 } , 0 \right) ;Directrix: x=−104x = - \frac { 10 } { 4 }
B) Vertex: (0,0) ;Focus: (110,0) \left( \frac { 1 } { 10 } , 0 \right) ;Directrix: x=110x = \frac { 1 } { 10 }
C) Vertex: (0,0) ;Focus: (−104,0) \left( - \frac { 10 } { 4 } , 0 \right) ;Directrix: x=−104x = - \frac { 10 } { 4 }
D) Vertex: (0,0) ;Focus: (−104,0) \left( - \frac { 10 } { 4 } , 0 \right) ;Directrix: x=104x = \frac { 10 } { 4 }
E) Vertex: (0,0) ;Focus: (−110,0) \left( - \frac { 1 } { 10 } , 0 \right) ;Directrix: x=110x = \frac { 1 } { 10 }

F) All of the above
G) B) and D)

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Find the standard form of the equation of the parabola and determine the coordinates of the focus. Find the standard form of the equation of the parabola and determine the coordinates of the focus. A) x ^ { 2 } = - 4 y ,focus: \left( 0 , - \frac { 1 } { 4 } \right) B) x ^ { 2 } = - \frac { 1 } { 16 } y ,focus: \left( 0 , - \frac { 1 } { 16 } \right) C) x ^ { 2 } = - \frac { 1 } { 4 } y ,focus: \left( 0 , - \frac { 1 } { 16 } \right) D) x ^ { 2 } = - 4 y ,focus: (0,-4) E) x ^ { 2 } = - \frac { 1 } { 4 } y ,focus: \left( 0 , - \frac { 1 } { 4 } \right)


A) x2=−4yx ^ { 2 } = - 4 y ,focus: (0,−14) \left( 0 , - \frac { 1 } { 4 } \right)
B) x2=−116yx ^ { 2 } = - \frac { 1 } { 16 } y ,focus: (0,−116) \left( 0 , - \frac { 1 } { 16 } \right)
C) x2=−14yx ^ { 2 } = - \frac { 1 } { 4 } y ,focus: (0,−116) \left( 0 , - \frac { 1 } { 16 } \right)
D) x2=−4yx ^ { 2 } = - 4 y ,focus: (0,-4)
E) x2=−14yx ^ { 2 } = - \frac { 1 } { 4 } y ,focus: (0,−14) \left( 0 , - \frac { 1 } { 4 } \right)

F) C) and E)
G) C) and D)

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The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure) .Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin. ) ​ The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure) .Write an equation for a cross section of the reflector.(Assume that the dish is directed upward and the vertex is at the origin. ) ​ a = 4.5 ​ A) x = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 18 x B) x ^ { 2 } = \frac { 1 } { 18 } y \text { or } y = 18 x ^ { 2 } C) x = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 4.5 x D) x ^ { 2 } = 18 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 } E) x ^ { 2 } = 4.5 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 } a=4.5a = 4.5 ​


A) x=118y2 or y2=18xx = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 18 x
B) x2=118y or y=18x2x ^ { 2 } = \frac { 1 } { 18 } y \text { or } y = 18 x ^ { 2 }
C) x=118y2 or y2=4.5xx = \frac { 1 } { 18 } y ^ { 2 } \text { or } y ^ { 2 } = 4.5 x
D) x2=18y or y=118x2x ^ { 2 } = 18 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 }
E) x2=4.5y or y=118x2x ^ { 2 } = 4.5 y \text { or } y = \frac { 1 } { 18 } x ^ { 2 }

F) B) and E)
G) A) and B)

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D

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