# How do you identity if the equation x^2=8y is a parabola, circle, ellipse, or hyperbola and how do you graph it?

Jan 27, 2018

It is a parabola opening up with vertex at $\left(0 , 0\right)$

#### Explanation:

Given -

${x}^{2} = 8 y$

It is a parabola opening up.
The general form of the equation of a parabola opening up is -

${x}^{2} = 4 a y$

Where -

$4$ is a constant
$a$ is the distance from the vertex to focus.
Its vertex is $\left(0 , 0\right)$

The given equation ${x}^{2} = 8 y$ can be written as -

${x}^{2} = 4 \times 2 \times y$