Answer:
y = 1/4 (x-4)² - 7
Step-by-step explanation:
Point (x , y) on the parabola, focus of (4, -8) and a directrix of y= -6
√(x-4)²+(y- -8)² = √(y- -6)²
(x-4)² + (y+8)² = (y+6)²
(y+8)² - (y+6)² = (x-4)²
(y²+16y+64) - (y²+12y+36) = (x-4)²
y²+16y+64-y²-12y-36 = 4y+28 = (x-4)²
4y = (x-4)² - 28
y = 1/4 (x-4)² - 7
standard formula of parabola: y = a(x-h)² + k (h,k): vertex (4,-7)
