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

Question

Quizplus · Accepted Answer

The given equation is in the form $(x - h)^2 = 4p(y - k)$, where the vertex is at $(h, k)$ and the focus is at $(h, k + p)$. Here, $h = -1$, $k = 2$, and $4p = 12$, so $p = 3$. Thus, the focus is at $(-1, 2 + 3) = (-1, 5)$. The directrix is $y = k - p = 2 - 3 = -1$, and the axis is $x = h = -1$.

Give the Focus, Directrix, and Axis for the Parabola (x+1)2=12(y−2)( x + 1 ) ^ { 2 } = 12 ( y - 2 )(x+1)2=12(y−2)

Give the Focus, Directrix, and Axis for the Parabola $( x + 1 ) ^ { 2 } = 12 ( y - 2 )$