What is the focus of the parabola given by the equation (y - 3) 2 = 8 (x - 5) ?

Vertex is (h, k) then

(y-k) ^2=4p (x-h)

so we have a parabola that opens left or right

p is distance from vertex to focus

ok, so if p is positive, tehen it opens to the right

the focus is to the right of the vertex

s

(y-3) ^2=4 (2) (x-5)

vertex is (5,3)

2 is positive so focus is to the right of vertex

it is 2 units from vertex

(5,3), move to right 2 units is 5+2=7

(7,3) is focus