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

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