Question

A parabola can be drawn given a focus of ( 6 , − 5 ) (6,−5) and a directrix of y = 1 y=1. Write the equation of the parabola in any form. -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12

Answer 1

y = -(1/12)(x -6)² -2

Explanation:

The vertex of the parabola is halfway between the focus and the directrix, so has y-coordinate (-5+1)/2 = -2. The difference in the y-coordinates between the focus and the vertex is ...

p = -5 -(-2) = -3

An equation of the parabola with vertex (h, k) and focus-vertex distance p can be written:

y = 1/(4p)(x -h)² +k

For (h, k) = (6, -2) and p = -3, the equation is ...

y = (-1/12)(x -6)² -2