Write an equation of a parabola with focus of (1,3) and directrix y = 5. show work
+128566 The directrix is 8 units below the focus
So...the vertex is ( 2, (6 + -2)/2 ) = (2, 4/2) = (2, 2)
And p is the distance between the vertex and directrix = [2 - (-2)] = 4
So....we have the form
4p(y - k) = (x - h)^2 where (h, k) is the vertex and p = 4
So we have
4(4)(y - 2) = (x - 2)^2
16 (y - 2) = (x - 2)^2
(y - 2) = (1/16)(x - 2)^2
y = (1/16)(x - 2) + 2
