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

Question

Quizplus · Accepted Answer

The vertex of the parabola is the origin (0,0). Since the coefficient of x is positive, the parabola opens to the right. The distance from the vertex to the focus is $\frac{1}{4}$ times the coefficient of x, which is $\frac{1}{4}(36) = 9$. Therefore, the focus is located at a point 9 units to the right of the vertex, which is (9,0). The directrix is a vertical line located $\frac{1}{4}$ times the coefficient of y units to the left of the vertex. Since there is no y term, the directrix is a vertical line at x = -9.

Find the Focus and Directrix of the Parabola y2=36xy ^ { 2 } = 36 xy2=36x

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