Question

What is the equation of the quadratic graph with a focus of (3, 4) and a directrix of y = 8?

Answer 1

I got f(x) = 1/2(x-3)^2 +6
Does that look right?

Answer 2

I mean 1/8 for the coefficient, oops.

Answer 3

one real simple way to approach this is to simply equate distances.

a parabola is defined as the collection of all points (x,y) that are the same distance from a focus point (a,b) and a line (a perpendicular distance) called a directrix (in this case y=8)



so we can simply setup the parabola as:

(x-a)^2 + (y-b)^2 = (x-x)^2 + (y-8)^2