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

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Answer 1 · 2017-05-27T11:22:11

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

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

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]

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