Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4961 miles and the polar radius Is 4687 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is at the Origin and that the trace formed by the plane $z = 0 \text { corresponds to the equator.) }$
A)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4961 ^ { 2 } } - \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 0$.
B)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4961 ^ { 2 } } - \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 0$
C)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } - \frac { y ^ { 2 } } { 4961 ^ { 2 } } - \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 1$
D)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4961 ^ { 2 } } + \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 1$
E)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4687 ^ { 2 } } + \frac { z ^ { 2 } } { 4961 ^ { 2 } } = 1$

Question

Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4961 miles and the polar radius Is 4687 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is at the Origin and that the trace formed by the plane $z = 0 \text { corresponds to the equator.) }$ 
A)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4961 ^ { 2 } } - \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 0$.
B)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4961 ^ { 2 } } - \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 0$
C)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } - \frac { y ^ { 2 } } { 4961 ^ { 2 } } - \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 1$
D)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4961 ^ { 2 } } + \frac { z ^ { 2 } } { 4687 ^ { 2 } } = 1$
E)$\frac { x ^ { 2 } } { 4961 ^ { 2 } } + \frac { y ^ { 2 } } { 4687 ^ { 2 } } + \frac { z ^ { 2 } } { 4961 ^ { 2 } } = 1$

Quizplus · Accepted Answer

The equation of an ellipsoid centered at the origin is given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$, where $a$, $b$, and $c$ are the radii along the x, y, and z axes, respectively. For an oblate ellipsoid, the equatorial radii (x and y axes) are equal and larger than the polar radius (z axis). Thus, with equatorial radius 4961 and polar radius 4687, the correct equation is $\frac{x^2}{4961^2} + \frac{y^2}{4961^2} + \frac{z^2}{4687^2} = 1$.

Some Planet Is an Oblate Ellipsoid Rather Than a Sphere z=0 corresponds to the equator.) z = 0 \text { corresponds to the equator.) }z=0 corresponds to the equator.)

Some Planet Is an Oblate Ellipsoid Rather Than a Sphere $z = 0 \text { corresponds to the equator.) }$