Question

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

Answer 1

y = -⅛(x - 3)² + 3

Explanation:

(x - h)² = 4p(y - k)

h = 3

k + p = 1

k - p = 5

2k = 6

k = 3

p = -2

(x - 3)² = 4(-2)(y - 3)

(x - 3)² = -8(y - 3)

y = -⅛(x - 3)² + 3