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What is an ellipse, what does it look like, and what is the formula for it?

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An ellipse is a shape somewhat similar to an oval. It could be a more "round" oval, close to a circle, or it could be a very long (and thin) oval.

Ellipse is one of the conic sections, which means it can be obtained by intersecting a cone with a plane slanted relatively to its base. The shape of the intersection is an ellipse.

The equation of an ellipse on a coordinate plane is

`(x-x_0)^2/a^2 + (y-y_0)^2/b^2 = 1` 

Here `(x_0, y_0)` are the coordinates of the center of the ellipse and a and b are the half-lengths of its axis. When a = b = r the ellipse becomes a circle with the radius r.

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