Find the focus and directrix of the parabola.
-$x ^ { 2 } = 36 y$
A) (9, 0); y = 9
B) (0, -9); x = - 9
C) (9, 0); x = 9
D) (0, 9); y = -9

Question

Quizplus · Accepted Answer

The given equation is $x^2 = 36y$, which is a vertical parabola opening upwards. The standard form of a vertical parabola is $x^2 = 4ay$, where the focus is at $(0, a)$ and the directrix is $y = -a$. Comparing $x^2 = 36y$ with $x^2 = 4ay$, we get $4a = 36$, so $a = 9$. Therefore, the focus is at $(0, 9)$ and the directrix is $y = -9$.

Find the Focus and Directrix of the Parabola x2=36yx ^ { 2 } = 36 yx2=36y

Find the Focus and Directrix of the Parabola $x ^ { 2 } = 36 y$