Posted by Lucy on Sunday, March 2, 2008 at 4:16pm.
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.

Algebra II  Damon, Sunday, March 2, 2008 at 4:48pm
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)
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