Find the equation of the parabola with vertex at $( 0,0 )$ and focus at $( 0,4 )$.
A) $\quad x ^ { 2 } = 16 y$
B) $\quad y ^ { 2 } = 16 x$
C) $\quad x ^ { 2 } = 4 y$
D) $x ^ { 2 } = y + 4$
E) none of these

Question

Quizplus · Accepted Answer

The vertex form of a parabola that opens upwards is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Here, $p = 4$, so the equation is $x^2 = 16y$.

Find the Equation of the Parabola with Vertex At (0,0)( 0,0 )(0,0)

Find the Equation of the Parabola with Vertex At $( 0,0 )$