Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $( 0 , - 4 )$
A) $x ^ { 2 } = 16 y$
B) $y ^ { 2 } = x$
C) $y ^ { 2 } = 16 x$
D) $x ^ { 2 } = - 16 y$
E) $y ^ { 2 } = - 16 x$

Question

Quizplus · Accepted Answer

The standard form of a parabola with its vertex at the origin and focus on the y-axis is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Here, the focus is at $(0, -4)$, so $p = -4$. Substituting $p = -4$ into the equation gives $x^2 = -16y$.

Find the Standard Form of the Equation of the Parabola (0,−4)( 0 , - 4 )(0,−4)

Find the Standard Form of the Equation of the Parabola $( 0 , - 4 )$