Precalculus Quiz and Discussion
danmelvanderson_i01c
quiz_w5.docxQUESTION 1
1. Find the vertices and locate the foci for the hyperbola whose equation is given. 81y2 - 64x2 = 5184
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vertices: (-8, 0), (8, 0) foci: (-, 0), (, 0) |
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vertices: (0, -8), (0, 8) foci: (0, -), (0, ) |
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vertices: (0, -9), (0, 9) foci: (0, -), (0, ) |
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vertices: (-9, 0), (9, 0) foci: (-, 0), (, 0) |
4 points
QUESTION 2
1. Find the vertices and locate the foci for the hyperbola whose equation is given. 49x2 - 16y2 = 784
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vertices: (-4, 0), (4, 0) foci: (-, 0), (, 0) |
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vertices: (0, -4), (0, 4) foci: (0, -), (0, ) |
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vertices: (-4, 0), (4, 0) foci: (-, 0), (, 0) |
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vertices: (-7, 0), (7, 0) foci: (-, 0), (, 0) |
4 points
QUESTION 3
1. Find the standard form of the equation of the hyperbola satisfying the given conditions. Center: (6, 5); Focus: (3, 5); Vertex: (5, 5)
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- (y - 6)2 = 1 |
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- (y - 5)2 = 1 |
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(x - 5)2 - = 1 |
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(x - 6)2 - = 1 |
4 points
QUESTION 4
1. 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 are both 6.25 inches tall and stand 50 inches apart. At some point along the road from the lowest point of the cable, the cable is 1 inches above the roadway. Find the distance between that point and the base of the nearest tower.
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10.2 in. |
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15 in. |
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9.8 in. |
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15.2 in. |
4 points
QUESTION 5
1. 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.
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4 in. |
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4.5 in. |
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6 in. |
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3.5 in. |
4 points
QUESTION 6
1. Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis vertical with length 16; length of minor axis = 6; center (0, 0)
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+ = 1 |
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+ = 1 |
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+ = 1 |
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+ = 1 |
4 points
QUESTION 7
1. Identify the equation as a parabola, circle, ellipse, or hyperbola. 12y = 3(x + 8)2
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Circle |
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Hyperbola |
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Parabola |
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Ellipse |
4 points
QUESTION 8
1. Find the vertices and locate the foci for the hyperbola whose equation is given. y = ±
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vertices: (0, -2), (0, 2) foci: (0, -2), (0, 2) |
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vertices: (-2, 0), (2, 0) foci: (-2, 0), (2, 0) |
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vertices: (-12, 0), (12, 0) foci: (-2, 0), (2, 0) |
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vertices: (-12, 0), (12, 0) foci: (-2, 0), (2, 0) |
4 points
QUESTION 9
1. Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -3 and 3
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+ = 1 |
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+ = 1 |
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+ = 1 |
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+ = 1 |
4 points
QUESTION 10
1. Find the standard form of the equation of the parabola using the information given. Vertex: (4, -7); Focus: (3, -7)
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(y + 7)2 = -4(x - 4) |
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(x + 4)2 = -16(y - 7) |
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(x + 4)2 = 16(y - 7) |
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(y + 7)2 = 4(x - 4) |
4 points
QUESTION 11
1. Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, -10), (0, 10); asymptote: y = x
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- = 1 |
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- = 1 |
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- = 1 |
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- = 1 |
4 points
QUESTION 12
1. Convert the equation to the standard form for a hyperbola by completing the square on x and y. 4y2 - 25x2 - 16y + 100x - 184 = 0
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- = 1 |
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- = 1 |
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- = 1 |
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- = 1 |
4 points
QUESTION 13
1. Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis horizontal with length 12; length of minor axis = 6; center (0, 0)
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+ = 1 |
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+ = 1 |
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+ = 1 |
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+ = 1 |
4 points
QUESTION 14
1. Find the standard form of the equation of the parabola using the information given. Focus: (3, 3); Directrix: y = -5
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(x - 3)2 = 16(y + 1) |
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(y + 1)2 = 16(x - 3) |
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(y - 3)2 = 16(x + 1) |
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(x + 1)2 = 16(y - 3) |
4 points
QUESTION 15
1. Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. x2 - 6x - 6y - 21 = 0
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(x + 3)2 = 6(y + 5) |
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(x - 3)2 = 6(y - 5) |
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(x - 3)2 = 6(y + 5) |
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(x + 3)2 = -6(y + 5) |
4 points
QUESTION 16
1. Convert the equation to the standard form for a hyperbola by completing the square on x and y. 4x2 - 25y2 - 8x + 50y - 121 = 0
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- = 1 |
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- = 1 |
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- = 1 |
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- = 1 |
4 points
QUESTION 17
1. Find the standard form of the equation of the parabola using the information given. Focus: (-3, -1); Directrix: x = 7
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(x - 2)2 = -20(y + 1) |
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(y + 1)2 = -20(x - 2) |
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(y - 2)2 = -20(x + 1) |
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(x + 1)2 = -20(y - 2) |
4 points
QUESTION 18
1. Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. y2 - 4y - 2x - 2 = 0
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(y - 2)2 = 2(x + 3) |
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(y + 2)2 = -2(x + 3) |
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(y + 2)2 = 2(x + 3) |
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(y - 2)2 = 2(x - 3) |
4 points
QUESTION 19
1. Identify the equation as a parabola, circle, ellipse, or hyperbola. 4x2 = 36 - 4y2
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Parabola |
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Hyperbola |
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Ellipse |
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Circle |
4 points
QUESTION 20
1. Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: (10, -3) and (-2, -3); endpoints of minor axis: (4, -1) and (4, -5)
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+ = 1 |
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+ = 1 |
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+ = 0 |
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+ = 1 |
4 points
QUESTION 21
1. Identify the equation as a parabola, circle, ellipse, or hyperbola. 2x = 2y2 - 30
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Ellipse |
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Circle |
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Parabola |
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Hyperbola |
4 points
QUESTION 22
1. Find the standard form of the equation of the hyperbola satisfying the given conditions. Endpoints of transverse axis: (-6, 0), (6, 0); foci: (-7, 0), (-7, 0)
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- = 1 |
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- = 1 |
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- = 1 |
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- = 1 |
4 points
QUESTION 23
1. Find the standard form of the equation of the ellipse satisfying the given conditions. Endpoints of major axis: and ; endpoints of minor axis: and
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+ = 1 |
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+ = 1 |
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+ = 1 |
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+ = 1 |
4 points
QUESTION 24
1. Identify the equation as a parabola, circle, ellipse, or hyperbola. (x - 2)2 = 16 - y2
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Circle |
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Ellipse |
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Hyperbola |
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Parabola |
4 points
QUESTION 25
1. Identify the equation as a parabola, circle, ellipse, or hyperbola. 9x2 = 4y2 + 36
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Hyperbola |
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Ellipse |
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Parabola |
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Circle |
