x=4+3sin9 and y=2+200s9 8 (3) Eliminate the parameter and write an equation in rectangular coordinates. (Hint: Solve for sine and cos. Square the result and apply the identity sinze + c0520 =1.) ECJmDe The equation in rectangular coordinates in standard form is D = 1 . (b) Sketch the curve and indicate its orientation. Given a circle where the center is (-2, 2) and another point on the circle is (-10, -4), (a) Write an equation of the circle in standard form. (b) Graph the circle. Part 1 of 2 (a) An equation of the circle in standard form is 0+0 0-0 0=0 X 5 Part 2 of 2 (b) Graph the circle. 18- O 16- 14- 12- 10 X 5 8 - -18 -16 -14 -12 -10 8 6 4 2 2 4 6 8 10 16 12 14 16 15 2 -6 -The reflective property of an ellipse is the principle behind "whispering galleries." These are rooms with elliptically shaped ceilings such that a person standing at one focus can hear even the slightest whisper spoken by another person standing at the other focus. A certain dome has a semielliptical ceiling, 94 ft long and 28 ft high. Choose a coordinate system so that the center of the semiellipse is (O, 0) with vertices (47, 0) and (47, 0) and with the ceiling at the middle of the room (0, 28). Approximately how far from the center along the major axis should each person be standing to hear the "whispering" effect? Round to 1 decimal place. Each person should be standing approximately m ft on either side of the center along the major axis to hear the whispering effect. 8 EE Write the standard form of an equation of an ellipse subject to the given conditions. Major axis parallel to the x-axis; Center: (1, 4); Length of major axis: 18 units; Length of minor axis: 14 units. The equation of the ellipse in standard form is D. Write the standard form of an equation of an ellipse subject to the given conditions. Vertices: (4, 0) and (-4, 0); Foci: (3, 0) and (3, 0) The equation of the ellipse in standard form is D