Question

What is the vertex form of the equation of the parabola with a focus at (17,14) and a directrix of `y=6`?

Answer 1

The equation of parabola in vertex form is `y=1/16(x-17)^2+10`

Explanation:

The vertex is at midpoint between focus`(17,14)` and directrix `y=6:.`The vertex is at`(17,(6+14)/2) or (17,10):.`The equation of parabola in vertex form is `y=a(x-17)^2+10`Distance of directrix from vertex is `d=(10-6)=4 :. a=1/(4d)=1/16:.`The equation of parabola in vertex form is `y=1/16(x-17)^2+10` graph{y=1/16(x-17)^2+10 [-80, 80, -40, 40]} [Ans]