Question

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.?

Answer 1

It's a parabola

Explanation:

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