Algebra II
posted by Lucy on .
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.

Since this parabola has vertex to the left and at the same level as the focus, it opens right and is of form:
(yk)^2 = 4 a (xh)
the vertex is at (h,k)
distance from vertex to focus = a
distance from vertex to directrix = a
here, vertex at (0,3)
so (y3)^2 = 4 a (x)
since a is distance from vertex to focus
(y3)^2 = 4*1 x = 4 x
so
x = (1/4)(y^2  6 y + 9)