# Circle is Curve of Second Degree

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## Theorem

The circle is a curve of degree $2$.

## Proof

From Equation of Circle in Cartesian Plane, a circle can be expressed in the form:

$x^2 + y^2 - 2 a x - 2 b y + a^2 + b^2 - R^2 = 0$

where $\tuple {a, b}$ is the center and $R$ is the radius.

This is a quadratic equation in $2$ variables.

Hence the result by definition of degree of curve.

$\blacksquare$