Answer:
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
Step-by-step explanation:
Given:
Focus of parabola: (-4, 6)
Directrix: y = 2
Required:
Equation for the parabola
SOLUTION:
Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.
Where,
a = -4
b = 6
k = 2
Plug these values into the equation formula
[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]
[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]
[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]
