Which is the equation of a parabola with directrix: y=−4 and focus (10,−6) ?

Question

Hi, I really need help. I am struggling.

Answer 1

maximum point is (10,-5) midpoint between focus (10,-6) and y=-4, (10,-5) = (h,k) in the equation

y=a(x-h)^2 + k

y=a(x-10)^2 -5 solve "a" the coefficient of (x-10)^2 by plugging in a 2nd point

find a point (x,-6) which is a distance = 2 below y=-4. then x-2 = 10, x=12 (12,-6)

-6=a(12-10)^2 = 4a

a =-3/2

y=-(3/2)(x-10)^2