# What is the equation of the parabola with a focus at (34,22) and a directrix of y= 32?

Equation of the parabola is $y = - \frac{1}{40} {\left(x - 34\right)}^{2} + 22$
The equation of the parabola with vertex at$\left(34 , 22\right)$ is $y = a {\left(x - 34\right)}^{2} + 22$ The directrix of $y = 32$ is behind the vertex. So The distance of directrix from vertex is $d = 32 - 22 = 10$. The parabola opens down, so $a$ is negative. We know $a = \frac{1}{4 d} = \frac{1}{40}$
Hence equation of the parabola is $y = - \frac{1}{40} {\left(x - 34\right)}^{2} + 22$ graph{-1/40(x-34)^2+22 [-160, 160, -80, 80]}[Ans]