Question

Write an equation for the parabola with focus (1,3) and vertex (0,3).

I cannot find any example in my book that works a problem with the vertex, all of the examples that I have to go by give only the focus and directrix.

Thanks.

Answer 1

Since this parabola has vertex to the left and at the same level as the focus, it opens right and is of form:

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

the vertex is at (h,k)
distance from vertex to focus = a
distance from vertex to directrix = a

here, vertex at (0,3)
so (y-3)^2 = 4 a (x)
since a is distance from vertex to focus
(y-3)^2 = 4*1 x = 4 x
so
x = (1/4)(y^2 - 6 y + 9)