The co-ordinates of the focus of Parabola x minus 3 power 2 is equal to 4 y minus 2 is Answer is 3 3 how?

Answer 1

The standard equation for an upward opening parabola with its vertex at (f,g) is (x - f)2 = 4c(y - g), where c is the focal length, that is the distance of the focus from the vertex.

Putting the equation shown in this form we have :-

(x - 3)2 = 4 * 1(y - 2) . . . thus c = 1

The vertex is at (3,2) and as the focal length is 1 (and this is positive) then the coordinates of the focus are (3, [2 + 1]) = (3,3).