Question

What is the vertex form of the equation of the parabola with a focus at (7,4) and a directrix of `y=3`?

Answer 1

The equation of Parabola is `y=1/2(x-7)^2+7/2`

Explanation:

The vertex is at mid point between focus and directrix so vertex is at `(7,3.5)`. The equaton of parabola in vertex form is `y=a(x-h)^2+k or y=a(x-7)^2+3.5` The distance of vertex from directrix is `0.5 ; :. a=1/(4*0.5)=1/2`So the equation is `y=1/2(x-7)^2+7/2` graph{1/2(x-7)^2+7/2 [-40, 40, -20, 20]}