In the equation [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex](adsbygoogle = window.adsbygoogle || []).push({});

can someone explain what those a and b are doing? I know they are the x and y intercepts of the graph, but why are we dividing x^2 and y^2 by them? Also, why are they squared? Why not just regular "a" and "b" like in the parabola equation?

The circle equation makes sense from the pythagorean theorem, but the a and b in the parabola, ellipse, and hyperbola equations really throw me off. Where did they come from? How did people know that if they want to get the U shape of a parabola or C shape of hyperbola or 0 shape of a ellipse that they should make these equations? The circle one is understandable to me since the set of every point that is a certain distance from a point will make a circle... I know my question doesn't make any sense but I can't seem to put into words what I am struggling with...

please help an idiot out!

Edit: why did the equation stack up vertically?

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# Need a little help understanding equation for an ellipse

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