posted by meg .
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.
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