how do u find the focus of a parbola?

Question

I HONESTLY HAVE NO IDEA HOW THIS DONE

(X-0)=-8(Y-0)

Answer 1

A parabola in the form x^2 = 2py has its vertex at the origin. If p is positive it "opens up" if p is negative it opens down. From the vertex, the focus would be located at a distance of p/2 in the direction that the parabola opens.
The same is true for a parabola in the form:
(x - a)^2 = 2p(y - b)
Except the vertex is at (a, b).
If you interchange the roles of x and y, all the above is true except 'opens up' would read 'opens to the right' and opens down would be opens to the left.

Answer 2

You did not write a parabola...so in general if the focus is c units from the vertex then the equation has the form ( )^2 = 4c( )...where c is measured on the axis of symmetry.....ex: (z - 10)^2 = 30 ( t +16) then 4c = 30..c = 7.5 and the focus is located at z = 10, t = -16 + 7.5