# How do you identify the following equation 3y^2 - x = 0 as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

Nov 9, 2015

It's a parabola

#### Explanation:

If you write the equation as $x = 3 {y}^{2}$, you can see that you are in the form $f \left(y\right) = 3 {y}^{2}$. This is a quadratic polynomial in $y$, which means that it represents a parabola with axis parallel to the $x$ axis.