Give the focus, directrix, and axis for the parabola.
-$$y ^ { 2 } = - 8 x$$
A) $( 0 , - 2 ) , y = 2 , y$-axis
B) $( 2,0 ) , x = - 2 , x$-axis
C) $( - 2,0 ) , y = 2 , y$-axis
D) $( - 2,0 ) , x = 2 , x$-axis

Question

Quizplus · Accepted Answer

The given equation is $y^2 = -8x$, which is a parabola that opens to the left. The standard form of a parabola opening to the left or right is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus and also from the vertex to the directrix. Here, $4p = -8$, so $p = -2$. The focus is at $(-2, 0)$, the directrix is $x = 2$, and the axis of symmetry is the $x$-axis, which matches option D.

Give the Focus, Directrix, and Axis for the Parabola y2=−8xy ^ { 2 } = - 8 xy2=−8x

Give the Focus, Directrix, and Axis for the Parabola $y ^ { 2 } = - 8 x$