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

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

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Answer 1 · 2015-11-09T11:16:58

It's a parabola

Explanation:

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

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

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