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

The equation of parabola is $y = \frac{1}{10} {\left(x - 12\right)}^{2} + 3.5$
Vertex is at equidistant from focus $\left(12 , 6\right)$ and directrix $\left(y = 1\right)$ So vertex is at $\left(12 , 3.5\right)$ The parabola opens up and the equation is $y = a {\left(x - 12\right)}^{2} + 3.5$. 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)=1/10Hence the equation of parabola is $y = \frac{1}{10} {\left(x - 12\right)}^{2} + 3.5$ graph{y=1/10(x-12)^2+3.5 [-40, 40, -20, 20]}[Ans]