Find an equation for the surface consisting of all points that are equidistant from the point $( 0 , - 2,0 )$ and the plane $y = 2$.
Select the correct answer.
A) $x ^ { 2 } + 8 y ^ { 2 } + z ^ { 2 } = 1$
B) $z ^ { 2 } - 8 y ^ { 2 } = x$
C) $z ^ { 2 } + x ^ { 2 } = - 8 y$
D) $z ^ { 2 } - x ^ { 2 } = - 8 y$
E) $x ^ { 2 } + y ^ { 2 } = 8 z$

Question

Quizplus · Accepted Answer

The equation of the surface is derived from the condition that the distance from a point $(x, y, z)$ to $(0, -2, 0)$ is equal to its distance to the plane $y = 2$. This results in the equation $\sqrt{x^2 + (y + 2)^2 + z^2} = |y - 2|$, which simplifies to $z^2 + x^2 = -8y$.

Find an Equation for the Surface Consisting of All Points (0,−2,0)( 0 , - 2,0 )(0,−2,0)

Find an Equation for the Surface Consisting of All Points $( 0 , - 2,0 )$