What is the equation of the quadratic graph with a focus of (5, 6) and a directrix of y = 2? f(x) = one eighth (x + 5)2 + 4 f(x) = −one eighth (x − 5)2 + 4 f(x) = one eighth (x − 5)2 + 4 f(x) = one eighth (x + 5)2 − 4
Accepted Solution
A:
In this problem, given the focus at (3, 1) and directrix at y = 5, then it is implied that the parabola is facing upwards. The vertex hence is at the middle of the focus and the directrix, hence at (3, 3). The general formula of the parabola is y-k = 4a ( x-h)^2. Substituting, y - 3 = 1/8 *(x-3)^2.