Question

My time is running out help!! MEDAL AND FAN!!

Find the focus of the parabola that has a vertex at (0, 0) and that passes through the points (–3, 3) and (3, 3).

Answer 1

use
4 p (y - k) = (x-h)^2 where (h,k) is the vertex
here (h,k) is (0,0) so you have
4p y = x^2

the point (3,3) is on the parabola. Put in x=3 and y=3 :
4 p *3 = 9
12p = 9
divide both sides by 12
p = 9/12
simplify (divide top and bottom by 3)
p= ¾

p is the distance from the vertex up to the focus.
i.e. the focus is at (0, 0+p) or (0, ¾)