Question

Derive the equation of a parabola given the focus is at (3,4) and the directrix is y=0 . Fill in the missing values of the equation in standard form.(1 point)
y=
x2−34x+258

Answer 1

Distance from (x,y) to focus (3,4) equals distance to directrix y=0:
sqrt((x−3)^2 + (y−4)^2) = y. Square both sides:
(x−3)^2 + (y−4)^2 = y^2
(x−3)^2 − 8y + 16 = 0 → 8y = (x−3)^2 + 16

So
y = (1/8)(x−3)^2 + 2 = (1/8)x^2 − (3/4)x + 25/8.