Find an equation of a parabola satisfying the given information

Question

Focus (6,4), directrix x= -7

Answer 1

recall that the parabola
y^2 = 4px
has
focus at (p,0)
vertex at (0,0)
directrix at x = -p
That is, the focus is 2p units away from the directrix.
Since your parabola's focus is 13 units away, p = 13/2
the axis is clearly y = 4, so the vertex is at (-1/2,4)
so the equation is
(y-4)^2 = 26(x + 1/2)