Find the vertex, focus, directrix, and focal width of the parabola.
-$$x = 8 y ^ { 2 }$$
A) Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 32 } , 0 \right) ;$ Directrix: $x = \frac { 1 } { 32 } ;$ Focal width: 32
B) Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 8 } , 0 \right) ;$ Directrix: $x = - \frac { 1 } { 8 } ;$ Focal width: $0.13$
C) Vertex: $( 0,0 )$; Focus: $\left( 0 , \frac { 1 } { 32 } \right) ;$ Directrix: $y = - \frac { 1 } { 32 }$; Focal width: 32
D) Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 32 } , 0 \right) ;$ Directrix: $x = - \frac { 1 } { 32 } ;$ Focal width: $0.13$

Question

Quizplus · Accepted Answer

The equation $x = 8y^2$ is a parabola that opens to the right. The vertex is at the origin $(0,0)$. The standard form is $x = 4py^2$, so $4p = 8$ gives $p = 2$. The focus is $(\frac{1}{32}, 0)$, the directrix is $x = -\frac{1}{32}$, and the focal width is 32.

Find the Vertex, Focus, Directrix, and Focal Width of the Parabola