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Question 1
Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.
x2 - 2x - 4y + 9 = 0
A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1
B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3
C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1
D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5

Question 2
Find the standard form of the equation of the following ellipse satisfying the given conditions.
Foci: (0, -4), (0, 4)
Vertices: (0, -7), (0, 7)
A. x2/43 + y2/28 = 1
B. x2/33 + y2/49 = 1
C. x2/53 + y2/21 = 1
D. x2/13 + y2/39 = 1

Question 3
Convert each equation to standard form by completing the square on x and y.
9x2 + 25y2 - 36x + 50y - 164 = 0
A. (x - 2)2/25 + (y + 1)2/9 = 1
B. (x - 2)2/24 + (y + 1)2/36 = 1
C. (x - 2)2/35 + (y + 1)2/25 = 1
D. (x - 2)2/22 + (y + 1)2/50 = 1

Question 4
Find the standard form of the equation of the following ellipse satisfying the given conditions.
Foci: (-2, 0), (2, 0)
Y-intercepts: -3 and 3
A. x2/23 + y2/6 = 1
B. x2/24 + y2/2 = 1
C. x2/13 + y2/9 = 1
D. x2/28 + y2/19 = 1

Question 5
Locate the foci and find the equations of the asymptotes.
x2/9 - y2/25 = 1
A. Foci: ({±√36, 0) ;asymptotes: y = ±5/3x
B. Foci: ({±√38, 0) ;asymptotes: y = ±5/3x
C. Foci: ({±√34, 0) ;asymptotes: y = ±5/3x
D. Foci: ({±√54, 0) ;asymptotes: y = ±6/3x
Question 6
Find the vertex, focus, and directrix of each parabola with the given equation.
(x - 2)2 = 8(y - 1)
A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1
B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1
C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1
D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1

Question 7
Find the vertices and locate the foci of each hyperbola with the given equation.
y2/4 - x2/1 = 1
A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)
B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)
C. Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)
D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)

Question 8
Find the standard form of the equation of each hyperbola satisfying the given conditions.
Center: (4, -2)
Focus: (7, -2)
Vertex: (6, -2)
A. (x - 4)2/4 - (y + 2)2/5 = 1
B. (x - 4)2/7 - (y + 2)2/6 = 1
C. (x - 4)2/2 - (y + 2)2/6 = 1
D. (x - 4)2/3 - (y + 2)2/4 = 1

Question 9
Locate the foci and find the equations of the asymptotes.
4y2 – x2 = 1
A. (0, ±√4/2); asymptotes: y = ±1/3x
B. (0, ±√5/2); asymptotes: y = ±1/2x
C. (0, ±√5/4); asymptotes: y = ±1/3x
D. (0, ±√5/3); asymptotes: y = ±1/2x

Question 10
Find the standard form of the equation of the following ellipse satisfying the given conditions.
Foci: (-5, 0), (5, 0)
Vertices: (-8, 0), (8, 0)
A. x2/49 + y2/ 25 = 1
B. x2/64 + y2/39 = 1
C. x2/56 + y2/29 = 1
D. x2/36 + y2/27 = 1

Question 11
Locate the foci of the ellipse of the following equation.
25x2 + 4y2 = 100
A. Foci at (1, -√11) and (1, √11)
B. Foci at (0, -√25) and (0, √25)
C. Foci at (0, -√22) and (0, √22)
D. Foci at (0, -√21) and (0, √21)

Question 12
Find the standard form of the equation of each hyperbola satisfying the given conditions.
Foci: (0, -3), (0, 3)
Vertices: (0, -1), (0, 1)
A. y2 - x2/4 = 0
B. y2 - x2/8 = 1
C. y2 - x2/3 = 1
D. y2 - x2/2 = 0

Question 13
Locate the foci and find the equations of the asymptotes.
x2/100 - y2/64 = 1
A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x
B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x
C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x
D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x

Question 14
Find the focus and directrix of each parabola with the given equation.
x2 = -4y
A. Focus: (0, -1), directrix: y = 1
B. Focus: (0, -2), directrix: y = 1
C. Focus: (0, -4), directrix: y = 1
D. Focus: (0, -1), directrix: y = 2

Question 15
Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.
y2 - 2y + 12x - 35 = 0
A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9
B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6
C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6
D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8

Question 16
Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: (7, 9) and (7, 3)
Endpoints of minor axis: (5, 6) and (9, 6)
A. (x - 7)2/6 + (y - 6)2/7 = 1
B. (x - 7)2/5 + (y - 6)2/6 = 1
C. (x - 7)2/4 + (y - 6)2/9 = 1
D. (x - 5)2/4 + (y - 4)2/9 = 1

Question 17
Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis vertical with length = 10
Length of minor axis = 4
Center: (-2, 3)
A. (x + 2)2/4 + (y - 3)2/25 = 1
B. (x + 4)2/4 + (y - 2)2/25 = 1
C. (x + 3)2/4 + (y - 2)2/25 = 1
D. (x + 5)2/4 + (y - 2)2/25 = 1

Question 19
Convert each equation to standard form by completing the square on x and y.
9x2 + 16y2 - 18x + 64y - 71 = 0
A. (x - 1)2/9 + (y + 2)2/18 = 1
B. (x - 1)2/18 + (y + 2)2/71 = 1
C. (x - 1)2/16 + (y + 2)2/9 = 1
D. (x - 1)2/64 + (y + 2)2/9 = 1

Question 20
Find the vertices and locate the foci of each hyperbola with the given equation.
x2/4 - y2/1 =1
A. Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)
B. Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)
C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)
D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)

• 6 years ago
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