Question

How would one write the equation of a parabola whose directrix is y=-6 and location of the focus is (-3,2)

Answer 1

F(-3,2)

V(-3,K)

D(-3,-6)

DV = VF,
K-(-6) = 2 - K,
K + 6 = 2 - K,
2K = 2 - 6 = -4,
K = -2.

V(-3,-2)

1/4a = DV = VF,
1/4a = 2-K,
1/4a = 2 - (- 2),
1/4a = 4,
16a = 1,
a = 1/16.

Y = a(x-h)^2 + k,
Eq: Y = 1/16(x+3)^2 -2. Vertex Form.