Write an equation of a parabola with focus of (1,3) and directrix y = 5. show work

Guest Mar 29, 2018

edited by
Guest
Mar 29, 2018

#1**+1 **

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

CPhill Mar 29, 2018