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# Lesson 3 (Mulit. Choice Questions)

Question 1 of 200.0/ 5.0 PointsHalley’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.A. 12.13 astronomical units; 1128 million milesB. 91.54 astronomical units; 8513 million milesC. 5.69 astronomical units; 529 million milesD. 6.06 astronomical units; 564 million milesQuestion 2 of 200.0/ 5.0 PointsUse the center, vertices, and asymptotes to graph the hyperbola.(x – 1)2 – 9(y – 2)2= 9A.B.C.D.Question 3 of 200.0/ 5.0 PointsFind the standard form of the equation of the ellipse and give the location of its foci.A. + = 1foci at (- , 0) and ( , 0)B. – = 1foci at (- , 0) and ( , 0)C. + = 1foci at (- , 0) and ( , 0)D. + = 1foci at (-7, 0) and ( 7, 0)Question 4 of 200.0/ 5.0 PointsRewrite the equation in a rotated x’y’-system without an x’y’ term. Express the equation involving x’ and y’ in the standard form of a conic section.31×2 + 10xy + 21y2-144 = 0A. x’2 = -4 y’B. y’2 = -4x’C. + = 1D. + = 1Question 5 of 200.0/ 5.0 PointsFind the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5A. + = 1B. + = 1C. + = 1D. + = 1Question 6 of 200.0/ 5.0 PointsFind the vertices and locate the foci for the hyperbola whose equation is given.49×2 – 100y2= 4900A. vertices: ( -10, 0), ( 10, 0)foci: (- , 0), ( , 0)B. vertices: ( -10, 0), ( 10, 0)foci: (- , 0), ( , 0)C. vertices: ( -7, 0), ( 7, 0)foci: (- , 0), ( , 0)D. vertices: (0, -10), (0, 10)foci: (0, – ), (0, )Question 7 of 205.0/ 5.0 PointsWrite the equation in terms of a rotated x’y’-system using θ, the angle of rotation. Write the equation involving x’ and y’ in standard form. xy +16 = 0; θ = 45°A. + = 1B. y’2 = -32x’C. + = 1D. – = 1Question 8 of 200.0/ 5.0 PointsWrite the appropriate rotation formulas so that in a rotated system the equation has no x’y’-term.10×2 – 4xy + 6y2- 8x + 8y = 0A. x = -y’; y = x’B. x = x’ – y’; y = x’ + y’C. x = (x’ – y’); y = (x’ + y’)D. x = x’ – y’; y = x’ + y’Question 9 of 200.0/ 5.0 PointsFind the location of the center, vertices, and foci for the hyperbola described by the equation.- = 1A. Center: ( -4, 1); Vertices: ( -10, 1) and ( 2, 1); Foci: and(B. Center: ( -4, 1); Vertices: ( -9, 1) and ( 3, 1); Foci: ( -3 + , 2) and ( 2 + , 2)C. Center: ( -4, 1); Vertices: ( -10, -1) and ( 2, -1); Foci: ( -4 – , -1) and ( -4 + , -1)D. Center: ( 4, -1); Vertices: ( -2, -1) and ( 10, -1); Foci: andQuestion 10 of 200.0/ 5.0 PointsSketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation’s domain and range.x = 2t, y = t2+ t + 3A. Domain: (-∞, ∞); Range: -1x, ∞)B. Domain: (-∞, ∞); Range: [ 2.75, ∞)C. Domain: (-∞, ∞); Range: [ 3, ∞)D. Domain: (-∞, ∞); Range: [ 2.75, ∞)Question 11 of 200.0/ 5.0 PointsUse vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.y = ±A. Asymptotes: y = ± xB. Asymptotes: y = ± xC. Asymptotes: y = ± xD. Asymptotes: y = ± xQuestion 12 of 200.0/ 5.0 PointsGraph the ellipse.16(x – 1)2 + 9(y + 2)2= 144A.B.C.D.Question 13 of 200.0/ 5.0 PointsIs the relation a function?y = x2+ 12x + 31A. YesB. NoQuestion 14 of 205.0/ 5.0 PointsDetermine the direction in which the parabola opens, and the vertex.y2= + 6x + 14A. Opens upward; ( -3, 5)B. Opens upward; ( 3, 5)C. Opens to the right; ( 5, 3)D. Opens to the right; ( 5, -3)Question 15 of 200.0/ 5.0 PointsMatch the equation to the graph.x2= 7yA.B.C.D.Question 16 of 200.0/ 5.0 Pointsy2= -2xA.B.C.D.Question 17 of 200.0/ 5.0 PointsConvert the equation to the standard form for a hyperbola by completing the square on x and y.x2 – y2+ 6x – 4y + 4 = 0A. (x + 3)2 + (y + 2)2 = 1B. – = 1C. (x + 3)2 – (y + 2)2 = 1D. (y + 3)2- (x + 2)2 = 1Question 18 of 200.0/ 5.0 PointsEliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2πA. x2 – y2 = 6; -6 ≤ x ≤ 6B. x2 – y2 = 36; -6 ≤ x ≤ 6C. x2 + y2 = 6; -6 ≤ x ≤ 6D. x2 + y2 = 36; -6 ≤ x ≤ 6Question 19 of 205.0/ 5.0 PointsConvert the equation to the standard form for a parabola by completing the square on x or y as appropriate.y2+ 2y – 2x – 3 = 0A. (y + 1)2 = 2(x + 2)B. (y – 1)2 = -2(x + 2)C. (y + 1)2 = 2(x – 2)D. (y – 1)2 = 2(x + 2)Question 20 of 200.0/ 5.0 PointsConvert the equation to the standard form for a hyperbola by completing the square on x and y.y2 – 25×2+ 4y + 50x – 46 = 0A. – (x – 2)2 = 1B. – (y – 1)2 = 1C. (x – 1)2 – = 1D. – (x – 1)2 = 1