Question

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

Answer 1

Focus is at `(-7,-9)`

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 `(y-k)^2 = -4a (x-h)` opening left .

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

So focus is at `(h+a),k or ( (-5-2), 9) or (-7,9)`
graph{(y-9)^2=-8(x+5) [-80, 80, -40, 40]} [Ans]