Question

Please show your work. I will give brainliest to the right answer!

Answer 1

Answer:

$y = \frac{1}{8}(x + 4)^2 + 4$

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

SOLUTION:

Using the formula, $y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k)$ , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

$y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2)$

$y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)$

$y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}$

$y = \frac{1}{8}(x + 4)^2 + 4$