Question

What is the equation in standard form of the parabola with a focus at (14,15) and a directrix of y= -7?

Answer 1

The equation of parabola is `y=1/88(x-14)^2+15`

Explanation:

The standard equation of parabola is `y=a(x-h)^2+k` where `(h,k)` is the vertex. So the equation of parabola is `y=a(x-14)^2+15` The distance of the vertex from the directrix `(y=-7)` is `15+7=22 :. a = 1/(4d)=1/(4*22)=1/88`. Hence equation of parabola is `y=1/88(x-14)^2+15` graph{1/88(x-14)^2+15 [-160, 160, -80, 80]}[Ans]