Question

What is the equation of the parabola with a focus at (34,22) and a directrix of y= 32?

Answer 1

Equation of the parabola is `y= -1/40(x-34)^2+22`

Explanation:

The equation of the parabola with vertex at`(34,22)` is `y=a(x-34)^2+22` The directrix of `y=32` is behind the vertex. So The distance of directrix from vertex is `d=32-22=10`. The parabola opens down, so `a` is negative. We know `a=1/(4d)=1/40`
Hence equation of the parabola is `y= -1/40(x-34)^2+22` graph{-1/40(x-34)^2+22 [-160, 160, -80, 80]}[Ans]