Question

Write the equation of a parabola with a vertex at (0,0), a focus at (2,0), and directrix x=-2

Answer 1

the directrix is x=-2, which means the parabola opens horizontally instead of vertically. The equation is (y - k)² = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p
in this case, h+p=2, k=0, and h-p=-2
solve for h and p: h=0, p=2
plug the numbers into the equation: (y-0)²=4*2(x-0)
simplify: y²=8x