Question

What is the vertex form of the equation of the parabola with a focus at (12,6) and a directrix of `y=1`?

Answer 1

The equation of parabola is `y=1/10(x-12)^2+3.5`

Explanation:

Vertex is at equidistant from focus `(12,6)` and directrix `(y=1)` So vertex is at `(12,3.5)` The parabola opens up and the equation is `y=a(x-12)^2+3.5`. The distance between vertex and directrix is `d=1/(4|a|) or a = 1/(4d) ; d=3.5-1=2.5 :.a = 1/(4*2.5)=1/10`Hence the equation of parabola is `y=1/10(x-12)^2+3.5` graph{y=1/10(x-12)^2+3.5 [-40, 40, -20, 20]}[Ans]