Question

Derive the equation of a parabola given the focus is at (-4, 6) and the directris is ar y = 8. Fill in the missing values of the equation in standard form. (1 point)
y= −14x2 −
x + 3

Answer 1

Directrix y = 8 and focus (-4, 6) give vertex at midpoint: (-4, 7). Distance p = 6 − 7 = −1. Vertex form:
(x + 4)^2 = 4p(y − 7) = −4(y − 7).

Solve for y:
y = 7 − 1/4 (x + 4)^2 = −1/4 x^2 − 2x + 3.

So the completed equation is y = −1/4 x^2 − 2x + 3.