Question

Directions: The focus and directrix of a parabola are given. Write an equation for each parabola.

(2,4) y = 6

May you explain the procedures on how to solve this equation? Please be detailed on each step.

Answer 1

I assume you have to use the basic definition of a parabola as the set of points equidistant from the focal point (2,4) and the line y=6

Make a sketch and let P(x,y) be any point on the parabola

so √((x-2)^2 + (y-4)^2) = √(y-6)^2

square both sides
(x-2)^2 + (y-4)^2 = (y-6)^2

x^2 - 4x + 4 + y^2 - 8y + 16 = y^2 - 12y + 36

y = -(1/4)x^2 + x + 4