Question

What is the equation of the parabola with a focus at (3,18) and a directrix of y= 17?

Answer 1

The equation of parabola is `y=1/2(x-3)^2+17.5`

Explanation:

The focus is at `(3,18)` .Directrix is `y=17`

The vertex is at equidistant from focus and directrix. So vertex is at `(3,17.5)`. Distance of directrix from vertex is `d=0.5:. a= 1/(4d)=1/(4*1/2)=1/2`

The standard equation of parabola is `y=a(x-h)^2+k ; (h,k)` being vertex. Here the directrix is behind vertex, so parabola opens upward and `a` is positive.

So the equation of parabola is `y=1/2(x-3)^2+17.5`
graph{1/2(x-3)^2+17.5 [-80, 80, -40, 40]} [Ans]