Question 5 l 11 points A searchlight is shaped like a paraboloid of revolution so that the light source (focus) is located 2 feet from the base (vertex) along the axis of symmetry. The searchlight's depth is 4 feet. A. A searchlight has been sketched in the space to the right. Label the dimensions as indicated in the problem. ' (worth 2 points) Convert the drawing into the sketch of a parabola on a Pr B. Cartesian Plane with the xaxis going from 7 to 7. scaled by 1. and the yaxis going from 1 to 6. scaled by 0.5. Put the vertex at the origin and orient the parabola so that it opens upward. (worth 3 points) C. Find an equation of the parabola you sketched in B. (worth 3 points) D. Determine the width of the searchlight at the top of its opening (to the nearest hundredth). (worth 3 points) Question 6 | 10 points The orbit of a planet about the sun is an ellipse, with the sun at one focus. The aphellon of a planet is its greatest distance from the sun, and the perihelion is its shortest distance. The mean distance of .a planet from the sun is half the length of the major axis of the elliptical orbit. A. illustrate the problem by drawing a pl'anet's'orblt around a sun, labeling the ' aphelion. perihelion, and the mean distance. (worth 3 points) .3. The mean distance of Mars from the sun is 142 million miles. If the perihelion of Mars is 128.5 million miles, what is the aplheI-ion? (worth 3 points) C. Write an equation for the orbit of Mars about the Sun. Place the center at the origin and the sun on the positive xaxis. You may leave- decimals in the denominator. (worth 4 points)