Question

What is the vertex form of the equation of the parabola with a focus at (2,-13) and a directrix of `y=23`?

Answer 1

The equation of parabola is `y=-1/72(x-2)^2+5`

Explanation:

The vertex is at midway between focus`(2,-13)`and directrix `y=23 :.`The vertex is at `2,5` The parabola opens down and the equation is `y= -a(x-2)^2+5` The vertex is at equidistance from focus and vertex and the distance is `d=23-5=18` we know `|a|=1/(4*d) :.a=1/(4*18)=1/72`Hence the equation of parabola is `y=-1/72(x-2)^2+5` graph{-1/72(x-2)^2+5 [-80, 80, -40, 40]}[Ans]