Find the standard form of the parabola with the given characteristic and vertex at the origin.
focus: $( 0 , - 5 )$
A) $x ^ { 2 } = - 20 y$
B) $x ^ { 2 } = - 5 y$
C) $x ^ { 2 } = 5 y$
D) $y ^ { 2 } = - 20 x$
E) $y ^ { 2 } = - 5 x$

Question

Quizplus · Accepted Answer

The standard form of a parabola with its vertex at the origin and a vertical axis is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Given the focus is at $(0, -5)$, $p = -5$, so the equation becomes $x^2 = -20y$.

Find the Standard Form of the Parabola with the Given (0,−5)( 0 , - 5 )(0,−5)

Find the Standard Form of the Parabola with the Given $( 0 , - 5 )$