Give the focus, directrix, and axis for the parabola.
-$$( x + 2 ) ^ { 2 } = - 28 ( y - 3 )$$
A) $( - 2 , - 4 ) , y = 10 , x = 3$
B) $( - 2 , - 4 ) , y = 10 , x = 4$
C) $( - 2 , - 4 ) , y = 10 , x = - 2$
D) $( - 9 , - 4 ) , y = 10 , x = - 2$

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 $x = h$. Here, $h = -2$, $k = 3$, and $4p = -28$, so $p = -7$. Thus, the focus is $(-2, 3 - 7) = (-2, -4)$, the directrix is $y = 3 + 7 = 10$, and the axis is $x = -2$.

Give the Focus, Directrix, and Axis for the Parabola (x+2)2=−28(y−3)( x + 2 ) ^ { 2 } = - 28 ( y - 3 )(x+2)2=−28(y−3)

Give the Focus, Directrix, and Axis for the Parabola $( x + 2 ) ^ { 2 } = - 28 ( y - 3 )$