Find the standard form of the equation of the parabola.
-Focus at $( 0,3 )$, directrix $y = - 3$
A) $y ^ { 2 } = 12 x$
B) $y ^ { 2 } = 3 x$
C) $y = \frac { 1 } { 3 } x ^ { 2 }$
D) $y = \frac { 1 } { 12 } x ^ { 2 }$

Question

Quizplus · Accepted Answer

The vertex form of a parabola with a vertical axis is $y = a(x-h)^2 + k$. The vertex is midway between the focus and directrix, so it is at $(0,0)$. The distance from the vertex to the focus is 3, so $a = \frac{1}{4p} = \frac{1}{12}$. Thus, the equation is $y = \frac{1}{12}x^2$.

Find the Standard Form of the Equation of the Parabola (0,3)( 0,3 )(0,3)

Find the Standard Form of the Equation of the Parabola $( 0,3 )$