What is the equation of the parabola with vertex (3,4) and focus (6,4)

This is a horizontal parabola that opens to the right.  I know this because the y-coordinate is the same for these two points and the focus is to the right of the vertex.

The basic equation for such a vertical parabola looks like

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

Since the vertex is (3,4), we now have  4p(x-3) = (y-4)^2.

p in this case is a positive number that is the difference between the x-coordinates of the vertex and focus:  this difference is 6-3, or 3.

Thus, 4p(x-3) = (y-4)^2   becomes   4(3)(x-3) = (y-4)^2, or

12(x-3) = (y-4)^2  (answer)

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