Question

A parabola can be drawn given a focus of left parenthesis, minus, 5, comma, 8, right parenthesis(−5,8) and a directrix of y, equals, minus, 4y=−4. What can be said about the parabola?
x
y
F (-5, 8)
directrix
Answer
Attempt 1 out of 2

The parabola has a vertex at (
,
), has a p-value of
and it
.

Answer 1

Vertex is midway between focus and directrix vertically: vertex = (-5, 2).
p = distance from vertex to focus = 6.
Since p > 0 (focus above directrix), the parabola opens upward.

Standard form: (x + 5)^2 = 4·6·(y − 2) = 24(y − 2).