Find the focus ,vertex and directrix of (y+5)^2=-6x+12

Question

how do I put this in y^2=4px form ?  John

Answer 1

You're really trying to put this in the form (y-k)² = 4p(x-h) where (h,k) is the vertex and p is the directed distance from th vertex to the focus.

 

So factor out the leading coefficient entirely to get

 

(y - -5)² = -6(x-2)

 

This makes the vertex (2,-5) and 4p=-6 so that p=-1.5

Since the y term is squared, the focus is 1.5 to the left of the vertex making it (.5,-5) and the

directrix is a vertical line 1.5 units to the right of the vertex making it x=3.5

 

Hope this helped