Find the focus and directrix of the parabola.
-$$y = 8 x ^ { 2 }$$
A) $\left( \frac { 1 } { 32 } , 0 \right) , x = - \frac { 1 } { 32 }$
B) $\left( 0 , \frac { 1 } { 32 } \right) , y = - \frac { 1 } { 32 }$
C) $\left( 0 , \frac { 1 } { 32 } \right) , y = \frac { 1 } { 32 }$
D) $\left( \frac { 1 } { 8 } , 0 \right) , x = - \frac { 1 } { 8 }$

Question

Quizplus · Accepted Answer

The given parabola is in the form $y = ax^2$, which is a vertical parabola. The focus is $(0, \frac{1}{4a})$ and the directrix is $y = -\frac{1}{4a}$. Here, $a = 8$, so the focus is $(0, \frac{1}{32})$ and the directrix is $y = -\frac{1}{32}$.

Find the Focus and Directrix of the Parabola y=8x2y = 8 x ^ { 2 }y=8x2

Find the Focus and Directrix of the Parabola $y = 8 x ^ { 2 }$