Find the equation of the parabola with latus rectum joining the points (3,5) and (3,-3)

Answer 1

you have the length of the L.R. = 8

The focus is (3,1)

Recall that the parabola

y^2 = 4px

has latus rectum 4p. The vertex is 2p from the focus.

So, your parabola is

(y-1)^2 = 8(x-1)

see

http://www.wolframalpha.com/input/?i=parabola+%28y-1%29^2+%3D+8%28x-1%29