# How do you identify the focus, directrix, and axis of symmetry of the parabola and graph the equation x^2= 40y?

Mar 19, 2017

The focus is $F = \left(0 , \frac{p}{2}\right) = \left(0 , 10\right)$
The directrix is $y = - 10$
The axis of symmetry is $x = 0$

#### Explanation:

We compare this equation ${x}^{2} = 40 y$ to

${x}^{2} = 2 p y$

$2 p = 40$

$p = 20$

The vertex is $V = \left(0 , 0\right)$

The focus is $F = \left(0 , \frac{p}{2}\right) = \left(0 , 10\right)$

The directrix is $y = - \frac{p}{2}$

$y = - 10$

The axis of symmetry is $x = 0$

graph{(x^2-40y)(y+10)((x-0)^2+(y-10)^2-0.1)=0 [-28.9, 28.83, -12.91, 15.96]}