Find the focus and directrix of the parabola.
-$$y ^ { 2 } - 16 x = 0$$
A) (4, 0); x = 4
B) (0, 4); y = -4
C) (4, 0); x = -4
D) (4, 0); y = -4

Question

Quizplus · Accepted Answer

The given equation of the parabola is $y^2 = 16x$. This is a rightward opening parabola with its vertex at the origin (0, 0). The standard form of a rightward opening parabola is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus, and also the distance from the vertex to the directrix. Comparing $y^2 = 16x$ with $y^2 = 4px$, we find $4p = 16$, so $p = 4$. Therefore, the focus is at (4, 0), and the directrix is the vertical line $x = -4$.

Find the Focus and Directrix of the Parabola y2−16x=0y ^ { 2 } - 16 x = 0y2−16x=0

Find the Focus and Directrix of the Parabola $y ^ { 2 } - 16 x = 0$