Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

Question

A. f(x) = −one eighth (x − 2)2 + 6
B. f(x) = one eighth (x − 2)2 + 6
C. f(x) = −one eighth (x + 2)2 + 8
D. f(x) = one eighth (x + 2)2 + 8

Answer 1

A is correct

it's a downward opening parabola so coefficient of the x^2 term is negative

vertex is half way between the directrix and focus, so it's (2,6)

f(x) = -(1/8)(x-2)^2 +6