Oval Shaped Cartesian Curves

In summary, there are different types of oval shaped Cartesian curves, including ellipses which have a specific equation and other types that may have higher degree equations. The specific equation for an ellipse is \frac{(x-x_0)^2}{a^2}+ \frac{(y-y_0)^2}{b^2}= 1, but other oval shaped curves may have equations that include higher degree functions and may not involve both x and y squared terms.
  • #1
mubashirmansoor
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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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  • #2
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.
 
  • #3


Hello, thank you for your question. Oval shaped Cartesian curves can have different degrees, not just +/- (x^2). They can also have other degrees such as +/- (x^3), +/- (x^4), etc. The degree of the curve will determine its shape and characteristics.
 

What are oval shaped cartesian curves?

Oval shaped cartesian curves are a type of mathematical curve that can be described using the Cartesian coordinate system. They typically have a rounded, elongated shape and are often used to model real-world phenomena such as orbits or trajectories.

What is the equation for an oval shaped cartesian curve?

The equation for an oval shaped cartesian curve can vary depending on the specific curve being described. However, in general, it can be written as (x/a)^2 + (y/b)^2 = 1, where a and b are constants that determine the shape and size of the curve.

What are some common applications of oval shaped cartesian curves?

Oval shaped cartesian curves have many practical uses in fields such as physics, engineering, and biology. They can be used to model the motion of planets and other celestial bodies, the trajectory of projectiles, and the growth of biological populations.

How do oval shaped cartesian curves differ from other types of curves?

Oval shaped cartesian curves have a distinct elongated, rounded shape that sets them apart from other types of curves. They also have a unique equation that includes both x and y variables, unlike other curves that may only involve one variable.

What are some real-world examples of oval shaped cartesian curves?

Some real-world examples of oval shaped cartesian curves include the path of a satellite orbiting the Earth, the trajectory of a cannonball being launched, and the population growth curve of a species. They can also be seen in the shapes of some fruits and vegetables, such as bananas and eggplants.

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