Question

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

Answer 1

Focus (-4,6) and directrix y = 8 ⇒ vertex is midway at (-4,7). With p = −1, standard form:
(x + 4)^2 = −4(y − 7).

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

So the missing coefficient is 2, and the equation is y = −1/4 x^2 − 2x + 3.