A parabola can be drawn given a focus of (10, 8)(10,8) and a directrix of x=-10x=−10. What can be said about the parabola?

Answer 1

focus (10,8) directrix x=-10

it's a rightward opening parabola with vertex half way between the focus & direction

vertex = (0,8)

x = a(y-8)^2, find one more point on the parabola to solve for "a" the leading coefficient

directly above the focus on the parabola is a point that is equidistant from the directrix and focus

(10,28)

x=a(y-k)^2 + h where (h,k)=vertex

10=a(28-8)^2+ 0

a = 10/400=1/40

the parabola is rightward opening

x=(1/40)(y-8)^2

It's domain is x>/=0

range is all real numbers