Question

Which is the equation of a parabola with a directrix at y = −3 and a focus at (−2, 3

Answer 1

Answer:  $y=\dfrac{1}{12}(x+2)^2$

Step-by-step explanation:

The vertex form of a parabola is: y = a(x - h)² + k    where

• (h, k) is the vertex
• $a=\dfrac{1}{4p}$

NOTE: p is the distance from the vertex to the focus.

The vertex is the midpoint between the focus and the directrix, so the vertex (h, k) = (-2, 0)

the distance from the vertex (-2, 0) to the focus (-2, 3) is 3 so p = 3

$a = \dfrac{1}{4(3)}=\dfrac{1}{12}$

Insert (h. k) = (-2, 0) and a = 1/12 into vertex form to get:

$y = \dfrac{1}{12}[x- (-2)]^2+0\quad \implies \quad \boxed{y=\dfrac{1}{12}(x+2)^2}$