Answer:
D
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant
Using the distance formula
[tex]\sqrt{(x+5)^2+(y-5)^2}[/tex] = | y + 1 |
Squaring both sides
(x + 5)² + (y - 5)² = (y + 1)^2 , that is
(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides
(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify
y² + 2y + 1 - y² + 10y - 25 = (x + 5)²
12y - 24 = (x + 5)² ← factor left side
12(y - 2) = (x + 5)² ← divide both sides by 12
y - 2 = [tex]\frac{1}{12}[/tex] (x + 5)² ← add 2 to both sides
y = [tex]\frac{1}{12}[/tex] (x + 5)² + 2
or
f(x) = [tex]\frac{1}{12}[/tex] (x + 5)² + 2 → D
