Are All Oval Shaped Cartesian Curves Limited to the Equation +/- (x^2)?

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SUMMARY

Oval-shaped Cartesian curves are not limited to the equation +/- (x^2). Ellipses, which are a specific type of oval, have the standard equation \(\frac{(x-x_0)^2}{a^2}+ \frac{(y-y_0)^2}{b^2}= 1\) when their axes are parallel to the x and y axes. Additionally, when axes are tilted, equations can include either x² or y², but not both, and must also incorporate the xy term. In a broader context, "oval" can refer to various closed paths that may utilize higher degree functions.

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Hello, are all Oval Shaped Cartesian Curves" +/-(x^2) " or we can have it with other degrees??
 
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mubashirmansoor said:
Hello, are all Oval Shaped Cartesian Curves" +/-(x^2) " or we can have it with other degrees??

I have no idea what you mean. It is true that every ellipse (including the special case of a circle), if that's what you mean by "oval", having axes parallel to the x and y- axes, has equation
[tex]\frac{(x-x_0)^2}{a^2}+ \frac{(y-y_0)^2}{b^2}= 1[/tex].
If you allow the axes to be tilted, then is possible to have an equation that has either x2 or y2 but not both (but then, of course, it must also include xy).

If you mean "oval" in the general sense of "any roughly eggshaped closed path" then it may have quite different equations- some involving higher degree functions.
 

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