Question
Find the equation of a parabola with vertex (3,1) and focus (5,1)
Answers
oobleck
note that the tw points lie on the same horizontal line. The parabola
y^2 = 4px has
vertex at (0,0)
focus at (p,0)
distance from focus to vertex = p.
So, shift this to (3,1) and p = 2
and you have
(y-1)^2 = 8(x-3)
See properties at
https://www.wolframalpha.com/input/?i=parabola+%28y-1%29%5E2+%3D+8%28x-3%29
y^2 = 4px has
vertex at (0,0)
focus at (p,0)
distance from focus to vertex = p.
So, shift this to (3,1) and p = 2
and you have
(y-1)^2 = 8(x-3)
See properties at
https://www.wolframalpha.com/input/?i=parabola+%28y-1%29%5E2+%3D+8%28x-3%29