The equation for a parabola with a focus at (-4, 3) and a directrix at y = 5 is; y = ¹/₄(x + 4)² + 4
The standard form of the equation of a parabola is given by;
(x - h)² = 4p(y - k)
where;
We are given the coordinates of the focus of the parabola as (-4, 3)
Thus, from (h, k + p)
h = -4
k + p = 3 ---- (eq 1)
From y = k - p, since it has a directrix of y = 5, then;
k - p = 5 ---- (eq 2)
→ Add equations (1) to (2) to get;
2k = 8
k = 8/2
k = 4
Put 4 for k in equation (1) to get
4 + p = 3
p = 4 - 3
p = 1
Plugging in the relevant values into the standard form of the equation of the parabola gives (x - h)² = 4p(y - k)
(x - (-4))² = 4(1)(y - 4)
⇒ (x + 4)² = 4(y - 4)
⇒ y = ¹/₄(x + 4)² + 4
The equation of the parabola is y = ¹/₄(x + 4)² + 4
Read more about equation of parabola at; https://brainly.com/question/4061870
