The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$y ^ { 2 } = - 24 x$$
A) focus: $( - 6,0 )$
directrix: $x = 6$
B) focus: $( 0 , - 6 )$
directrix: $y = 6$
C) focus: $( 6,0 )$
directrix: $x = - 6$
D) focus: $( - 6,0 )$
directrix: $\mathrm { y } = 6$

Question

Quizplus · Accepted Answer

The equation $y^2 = -24x$ represents a parabola that opens to the left with its vertex at the origin (0,0). The focus of such a parabola is located at $(-\frac{1}{4}a, 0)$, where $a$ is the coefficient of $x$ in the equation. Here, $a = -24$, so the focus is at $(-6, 0)$ because $-\frac{1}{4} \times -24 = 6$. The directrix is a vertical line opposite the direction of the opening of the parabola, which is $x = 6$.

The Parabola 1 Graph Parabolas with Vertices at the Origin y2=−24xy ^ { 2 } = - 24 xy2=−24x

The Parabola
1 Graph Parabolas with Vertices at the Origin $y ^ { 2 } = - 24 x$