Question 21
Find the solution set for each system by finding points of intersection.
x2 + y2 = 1
x2 + 9y = 9
Find the solution set for each system by finding points of intersection.
x2 + y2 = 1
x2 + 9y = 9
A. {(0, -2), (0, 4)}
B. {(0, -2), (0, 1)}
C. {(0, -3), (0, 1)}
D. {(0, -1), (0, 1)}
There is no correct alternative. (0, 1) is the only intersection point.
Question 22
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 23
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 24
Find the vertex, focus, and directrix of each parabola with the given equation.
(y + 1)2 = -8x
A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2
B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3
C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1
D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5
Question 25
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 26
Find the standard form of the equation of each hyperbola satisfying the given conditions.
Endpoints of transverse axis: (0, -6), (0, 6)
Asymptote: y = 2x
A. y2/6 - x2/9 = 1
B. y2/36 - x2/9 = 1
C. y2/37 - x2/27 = 1
D. y2/9 - x2/6 = 1
Question 27
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 28
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 29
Locate the foci of the ellipse of the following equation.
7x2 = 35 - 5y2
A. Foci at (0, -√2) and (0, √2)
B. Foci at (0, -√1) and (0, √1)
C. Foci at (0, -√7) and (0, √7)
D. Foci at (0, -√5) and (0, √5)
Question 30
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 31
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 32
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 33
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 34
Find the vertex, focus, and directrix of each parabola with the given equation.
(y + 3)2 = 12(x + 1)
A. Vertex: (-1, -3); focus: (1, -3); directrix: x = -3
B. Vertex: (-1, -1); focus: (4, -3); directrix: x = -5
C. Vertex: (-2, -3); focus: (2, -4); directrix: x = -7
D. Vertex: (-1, -3); focus: (2, -3); directrix: x=-4
Question 35
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 36
Convert each equation to standard form by completing the square on x and y.
4x2 + y2 + 16x - 6y - 39 = 0
A. (x + 2)2/4 + (y - 3)2/39 = 1
B. (x + 2)2/39 + (y - 4)2/64 = 1
C. (x + 2)2/16 + (y - 3)2/64 = 1
D. (x + 2)2/6 + (y - 3)2/4 = 1
Question 37
Find the focus and directrix of the parabola with the given equation.
8x2 + 4y = 0
A. Focus: (0, -1/4); directrix: y = 1/4
B. Focus: (0, -1/6); directrix: y = 1/6
C. Focus: (0, -1/8); directrix: y = 1/8
D. Focus: (0, -1/2); directrix: y = 1/2
Question 38
Find the vertex, focus, and directrix of each parabola with the given equation.
(x + 1)2 = -8(y + 1)
A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1
B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1
C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1
D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1
Question 39
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 40
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
