Find the vertex, focus, directrix, and focal width of the parabola.
-$$y ^ { 2 } = - 12 x$$
A) Vertex: $( 0,0 )$; Focus: $( 3,0 )$; Directrix: $x = - 3$; Focal width: 3
B) Vertex: $( 0,0 )$; Focus: $( - 3,0 )$; Directrix: $y = 3$; Focal wid th: 48
C) Vertex: $( 0,0 )$; Focus: $( 0 , - 3 )$; Directrix: $y = 3$; Focal width: 48
D) Vertex: $( 0,0 )$; Focus: $( - 3,0 )$; Directrix: $x = 3$; Focal width: 12

Question

Quizplus · Accepted Answer

The equation $y^2 = -12x$ represents a parabola that opens to the left with its vertex at the origin $(0,0)$. The coefficient of $x$ is $-12$, indicating a focal distance of $3$ (since $4p = -12$, thus $p = -3$). The focus is therefore $(-3,0)$, and the directrix is a vertical line $x = 3$. The focal width, given by $4|p|$, is $12$.

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