Question 1 of 20
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Halley’s comet has an elliptical orbit with the sun at one focus. Its orbit shown below is given approximately by
In the formula, r is measured in astronomical units. (One astronomical unit is the average distance from Earth to the sun, approximately 93 million miles.) Find the distance from Halley’s comet to the sun at its greatest distance from the sun. Round to the nearest hundredth of an astronomical unit and the nearest million miles.
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A. 12.13 astronomical units; 1128 million miles |
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B. 91.54 astronomical units; 8513 million miles |
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C. 5.69 astronomical units; 529 million miles |
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D. 6.06 astronomical units; 564 million miles |
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Question 2 of 20
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Use the center, vertices, and asymptotes to graph the hyperbola.
(x – 1)
2 – 9(y – 2)
2= 9
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Question 3 of 20
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Question 4 of 20
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Question 5 of 20
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Question 6 of 20
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Find the vertices and locate the foci for the hyperbola whose equation is given.
49x
2 – 100y
2= 4900
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A. vertices: ( -10, 0), ( 10, 0) foci: (- , 0), ( , 0) |
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B. vertices: ( -10, 0), ( 10, 0) foci: (- , 0), ( , 0) |
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C. vertices: ( -7, 0), ( 7, 0) foci: (- , 0), ( , 0) |
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D. vertices: (0, -10), (0, 10) foci: (0, – ), (0, ) |
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Question 7 of 20
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Question 8 of 20
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Question 9 of 20
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Find the location of the center, vertices, and foci for the hyperbola described by the equation.
–
= 1
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A. Center: ( -4, 1); Vertices: ( -10, 1) and ( 2, 1); Foci: and ( |
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B. Center: ( -4, 1); Vertices: ( -9, 1) and ( 3, 1); Foci: ( -3 + , 2) and ( 2 + , 2) |
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C. Center: ( -4, 1); Vertices: ( -10, -1) and ( 2, -1); Foci: ( -4 – , -1) and ( -4 + , -1) |
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D. Center: ( 4, -1); Vertices: ( -2, -1) and ( 10, -1); Foci: and |
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Question 10 of 20
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Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation’s domain and range.
x = 2t, y = t
2+ t + 3
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Question 11 of 20
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Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
y = ±
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Question 12 of 20
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Graph the ellipse.
16(x – 1)
2 + 9(y + 2)
2= 144
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