Question

A parabola can be drawn given a focus of left parenthesis, minus, 3, comma, minus, 6, right parenthesis(−3,−6) and a directrix of x, equals, 7x=7. What can be said about the parabola?
x
y
F (-3, -6)
directrix
Answer
Attempt 1 out of 2

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

Answer 1

The vertex is midway between the focus and the directrix: ((-3+7)/2, -6) = (2, -6). The axis is the horizontal line y = -6. The signed focal parameter p = focus_x − vertex_x = −3 − 2 = −5 (|p| = 5), so the parabola opens left. Equation in standard form:

(y + 6)^2 = 4p(x − 2) = −20(x − 2).