topic: Ellipses

10. [-/1 Points] DETAILS SPRECALC7 11.2.032.MI. MY NOTES ASK YOUR TEACHER Find an equation for the ellipse whose graph is shown. 4 F(0, 3) X 0 # Show My Work (Optional)11. [-/1 Points] DETAILS SPRECALC7 11.2.033. MY NOTES ASK YOUR TEACHER Find an equation for the ellipse whose graph is shown. (10, 5) 0 15 X + Show My Work (Optional) ?13. [0/1 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.2.044. MY NOTES ASK YOUR TEACHER Find an equation for the ellipse that satisfies the given conditions. Foci: F(+\\ 20, 0), vertices: ($5, 0) X # Show My Work (Optional) Submit Answer 14. [-/1 Points] DETAILS SPRECALC7 11.2.046.MI. MY NOTES ASK YOUR TEACHER Find an equation for the ellipse that satisfies the given conditions. Length of major axis: 14, length of minor axis: 12, foci on x-axis, centered at the origin15. [-/1 Points] DETAILS SPRECALC7 11.2.050.MI. MY NOTES ASK YOUR TEACHER Find an equation for the ellipse that satisfies the given conditions. Endpoints of minor axis: (0, +4), distance between foci: 10 # Show My Work (Optional) @ 16. [-/1 Points] DETAILS SPRECALC7 11.2.052. MY NOTES ASK YOUR TEACHER Find an equation for the ellipse that satisfies the given conditions. Length of minor axis: 12, foci on y-axis, ellipse passes through the point (v 6, v50), centered at the origin+ Show My Work (Optional) ? 17. [-/1 Points] DETAILS SPRECALC7 11.2.056. MY NOTES ASK YOUR TEACHER Find an equation for the ellipse that satisfies the given conditions. Eccentricity: V3/5, foci on x-axis, length of major axis: 20, centered at the origin Show My Work (Optional)18. [l2 Points] SPRECALC711.2,061.MI. ASK YOUR TEACHER The ancillary circle of ah ellipse is the circle with radius equal to half the length of the minor axis and center the same as the ellipse (see the gure). The ancillary circle is thus the largest circle that can t within an ellipse ellipse ancillary circle (a) Find ah equation far the ancillary circle of the ellipse x2 + 64y2 = 256. (b) For the ellipse and ancillary circle of part (a), show that if (s, t) is a poiht on the ancillary circle, then (851 t) is a point on the ellipse This answer has not been graded yet 20. [l2 Points] SPRECALC711.2,068.MI. ASK YOUR TEACHER A carpenter wishes to construct an elliptical table top from a 8 ft by 16 ft sheet of plywood. He will trace out the ellipse using the "thumbtack and string" method illustrated in Figures I and I]. What length of string should he use, and how far apart should the tacks be located, if the ellipse is to be the largest possible that can be cut out of the plywood sheet? (Round your answers to two decimal places.) m :n long 1.1) [bl Figure I Figure 11 21. [I1 Paints] SPRECALC711.2.069.MI. ASK YOUR TEACHER A "sunburst" window above a doorway is constructed in the shape of the top half of an ellipse, as shown in the gure. The window is b = 40 in. tall at its highest point and a = 70 in. wide at the bottom. Find the height of the window x = 28 in. from the center of the base. (Round your answer to one decimal place.) Show My Work [ammo 23. [2/8 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 11.4.006.MI. MY NOTES ASK YOUR TEACHER An equation of an ellipse is given. ( x - 5 )2 + (y + 5)2 = 1 9 (a) Find the center, vertices, and foci of the ellipse. center (x, y) = 5, - 5 focus ( x, y ) = (smaller x-value) X focus ( x, y ) = ( (larger x-value) X vertex (x, y) = ( (smaller x-value) X vertex ( x , y ) = (larger x-value) X (b) Determine the lengths of the major and minor axes. major axis units minor axis units (c) Sketch a graph of the ellipse. 10/ 1024. [-/8 Points] DETAILS SPRECALC7 11.4.010. MY NOTES ASK YOUR TEACHER An equation of an ellipse is given. ( x + 1) 2 + ( y + 1)2 = 1 25 64 (a) Find the center, vertices, and foci of the ellipse. center ( x, y ) = ( focus (x, y) = (smaller y-value) focus (x, y) = (larger y-value) vertex ( x , y ) = (smaller y-value) vertex ( x , y ) = (larger y-value) (b) Determine the lengths of the major and minor axes. major axis units minor axis units (c) Sketch a graph of the ellipse. - 4 10/ 1025. [-/8 Points] DETAILS SPRECALC7 11.4.011. MY NOTES ASK YOUR TEACHER An equation of an ellipse is given. 16x2 + 36y2 - 72y = 540 (a) Find the center, vertices, and foci of the ellipse. center (x, y) =( focus ( x, y ) = ( (smaller x-value) focus ( x, y) = ( (larger x-value) vertex (x, y) =( (smaller x-value) vertex (x, y) =( (larger x-value) (b) Determine the lengths of the major and minor axes. major axis units minor axis units (c) Sketch a graph of the ellipse. 10 1026. [-/8 Points] DETAILS SPRECALC7 11.4.012. MY NOTES ASK YOUR TEACHER An equation of an ellipse is given. 9x2 - 54x + y2 + 2y + 46=0 (a) Find the center, vertices, and foci of the ellipse. center (x, y) = focus ( x , y ) = (smaller y-value) focus ( x, y ) = ( (larger y-value) vertex (x, y ) = (smaller y-value) vertex ( x , y ) = (larger y-value) (b) Determine the lengths of the major and minor axes. major axis units minor axis units (c) Sketch a graph of the ellipse. 10- 1027. [-/1 Points] DETAILS SPRECALC7 11.4.032.MI. MY NOTES ASK YOUR TEACHER Find an equation for the conic whose graph is shown. 4 X 1 2 3 4 5 6 7 8 9 10 11 12 -12 Show My Work (Optional)28. [-/1 Points] DETAILS SPRECALC7 11.4.035. MY NOTES ASK YOUR TEACHER Find an equation for the conic section with the given properties. The ellipse with center C(1, -3), vertices Vi(-9, -3) and V2(11, -3), and foci F1(-5, -3) and F2(7, -3) Show My Work (Optional) 29. [-/1 Points] DETAILS SPRECALC7 11.4.043. MY NOTES ASK YOUR TEACHER Find an equation for the conic section with the given properties. The ellipse with foci F1(4, -3) and F2(6, -3) that passes through the point (5, 1) Show My Work (Optional) ?30. [-/1 Points] DETAILS SPRECALC7 11.4.044. MY NOTES ASK YOUR TEACHER Find an equation for the conic section with the given properties. The ellipse with foci F1(2, -4) and F2(2, 4), and x-intercepts 0 and 4 Show My Work (Optional) ? 31. [-/1 Points] DETAILS SPRECALC7 11.4.067. MY NOTES ASK YOUR TEACHER A satellite is in an elliptical orbit around the earth with the center of the earth at one focus, as shown in the figure. The height of the satellite above the earth varies between 150 mi and 430 mi. Assume that the earth is a sphere with radius 3960 mi. Find an equation for the path of the satellite with the origin at the center of the earth. (Assume the elliptical orbit of the satellite lies in the xy coordinate plane with a focus at the origin and the other focus lying on the negative x axis.) 430 mi 150 mi