# What is the focus of the parabola (y-9)^2 = -8(x+5)?

May 27, 2017

Focus is at $\left(- 7 , - 9\right)$

#### Explanation:

(y-9)^2 = -8 (x+5) or (y-9)^2 = -4 *2 (x+5) ; h= -5 , k =9 , a = -2 .

This is a parabola of standard equation ${\left(y - k\right)}^{2} = - 4 a \left(x - h\right)$ opening left .

Vertex is at $\left(h , k\right) i . e \left(- 5 , 9\right)$ . Focus is at "$a$" distance left of vertex.

So focus is at $\left(h + a\right) , k \mathmr{and} \left(\left(- 5 - 2\right) , 9\right) \mathmr{and} \left(- 7 , 9\right)$
graph{(y-9)^2=-8(x+5) [-80, 80, -40, 40]} [Ans]