Locus & The Parabola help (1 Viewer)

[j1mmy_]

The latus rectum of a parabola has endpoints (-2, 3) and (6, 3). Find two possible equations for the parabola.

All I've done is found the equation of the latus rectum, which is y = 3. I'm not sure what to do next.

Answers are:
x²-4x-8y+12= 0 and x²-4x+8y-36= 0

 

[TimeGoesTooFast]

Lol I know who you are But:

For these questions, you have to split it into cases

Given that the endpoints are (-2,3) and (6,3) -> the y ordinates don't change meaning that the equation of the parabola is in the form (x-k)^2 = +- 4a(y-k)
Latus rectum length =4a = 6--2 =8
Sub that in and one of the endpoints and you should get the value of k
Then expand and move everything around; should get it.