Find the vertex, focus, directrix, and focal width of the parabola.
-$$\mathrm { y } ^ { 2 } = 32 \mathrm { x }$$
A) Vertex: $( 0,0 )$; Focus: $( 8,0 )$; Directrix: $x = - 8$; Focal width: 128
B) Vertex: $( 0,0 )$; Focus: $( 0,8 )$; Directrix: $y = - 8$; Focal width: 8
C) Vertex: $( 0,0 )$; Focus: $( 8,0 )$; Directrix: $x = - 8$; Focal width: 32
D) Vertex: $( 0,0 )$; Focus: $( 8,8 )$; Directrix: $x = 8$; Focal width: 128

Question

Quizplus · Accepted Answer

The equation $y^2 = 32x$ is in the form $y^2 = 4px$, where $p = 8$, indicating the parabola opens to the right with vertex at the origin (0,0), focus at (8,0), directrix $x = -8$, and focal width $4p = 32$.

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