A certain lunar crater is shaped approximately as a parabolo

A certain lunar crater is shaped approximately as a paraboloid (see figure). The cross sections of the crater parallel to the lunar surface are circular, with a maximum radius of 60 meters. The depth of the crater is 9 meters. Find an equation for the surface of the crater. [Write your equation such that the bottom of the crater is located at (x, y, z) = (0, 0, 0). Assume the z-axis is perpendicular to the lunar surface.] Please show your work \\ explain your answer

Solution

Fourth option has the required profile