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

[mubashirmansoor]

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

 

[HallsofIvy]

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
\frac{(x-x_0)^2}{a^2}+ \frac{(y-y_0)^2}{b^2}= 1.
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.