Give the focus, directrix, and axis for the parabola.
-$$( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$$
A) $( - 2 , - 1 ) , y = 11 , x = 5$
B) $( - 2 , - 1 ) , y = 11 , x = - 2$
C) $( - 8 , - 1 ) , y = 11 , x = - 2$
D) $( - 2 , - 1 ) , y = 11 , x = 6$

Question

Quizplus · Accepted Answer

The given equation is in the form $(x - h)^2 = 4p(y - k)$, where the vertex is at $(h, k)$, the focus is at $(h, k + p)$, and the directrix is $y = k - p$. Here, $h = -2$, $k = 5$, and $4p = -24$, so $p = -6$. Thus, the focus is $(-2, 5 - 6) = (-2, -1)$, and the directrix is $y = 5 + 6 = 11$. The axis of symmetry is $x = h = -2$.

Give the Focus, Directrix, and Axis for the Parabola (x+2)2=−24(y−5)( x + 2 ) ^ { 2 } = - 24 ( y - 5 )(x+2)2=−24(y−5)

Give the Focus, Directrix, and Axis for the Parabola $( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$