Give the focus, directrix, and axis for the parabola.
-$$( y - 8 ) ^ { 2 } = - 12 ( x + 4 )$$
A) $( - 7,8 ) , x = - 1 , y = - 4$
B) $( - 7,8 ) , x = - 4 , y = 8$
C) $( - 7,5 ) , x = - 1 , y = 8$
D) $( - 7,8 ) , x = - 1 , y = 8$

Question

Quizplus · Accepted Answer

The given equation is in the form $(y-k)^2 = 4p(x-h)$, where the vertex is at $(h, k)$ and the focus is at $(h+p, k)$. Here, $h = -4$, $k = 8$, and $4p = -12$, so $p = -3$. The focus is at $(-4-3, 8) = (-7, 8)$, the directrix is $x = h-p = -4+3 = -1$, and the axis is $y = 8$.

Give the Focus, Directrix, and Axis for the Parabola (y−8)2=−12(x+4)( y - 8 ) ^ { 2 } = - 12 ( x + 4 )(y−8)2=−12(x+4)

Give the Focus, Directrix, and Axis for the Parabola $( y - 8 ) ^ { 2 } = - 12 ( x + 4 )$