Give the focus, directrix, and axis for the parabola.
-$$( x + 5 ) ^ { 2 } = - 20 ( y - 4 )$$
A) $( - 5 , - 1 ) , y = 9 , x = - 5$
B) $( - 5 , - 1 ) , y = 9 , x = 5$
C) $( - 5 , - 1 ) , y = 9 , x = 4$
D) $( - 10 , - 1 ) , y = 9 , x = - 5$

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 $(h, k + p)$, the directrix is $y = k - p$, and the axis of symmetry is $x = h$. For the given equation $(x + 5)^2 = -20(y - 4)$, we have $h = -5$, $k = 4$, and $4p = -20$, so $p = -5$. Therefore, the focus is $(-5, 4 - 5) = (-5, -1)$, the directrix is $y = 4 + 5 = 9$, and the axis of symmetry is $x = -5$.

Give the Focus, Directrix, and Axis for the Parabola (x+5)2=−20(y−4)( x + 5 ) ^ { 2 } = - 20 ( y - 4 )(x+5)2=−20(y−4)

Give the Focus, Directrix, and Axis for the Parabola $( x + 5 ) ^ { 2 } = - 20 ( y - 4 )$