A satellite is in elliptical orbit around the earth with the center of the earth at one focus. The height of the satellite above the earth varies between 140 miles and 440 miles. Assume the earth is a sphere with radius of 3960 miles. Find an equation for the path of the satellite with the origin at the center of the earth.

3. Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of the hyperbola nearest the spacecraft's path is the center of Jupiter. The diameter of the planet is 139,822 km. Suppose the path of an approaching spacecraft has an equation with a = 80,000 km and c= 170,000 Km. Assuming the transverse axis.js horizontal, write the equation that models the path of the spacecraft as it approaches Jupiter. What is the distance from the spacecraft to the planet at the vertex of the hyperbola?

Use these parametric equations to graph the ellipse when a=  3 and b= 1, 2, 4, and 8.

Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse axis 6 and the curve passes through the point (7, -4).