Cardioid的经过一点的切线个数

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P为平面上一点, 证明$ (x^2+y^2+x)^2=x^2+y^2$的经过一点P的切线个数是1,2或3, 分别当P在曲线内,上或外.

Cardiod $\in$ Epicycloid
Cardioid Evolute is a mirror-image cardioid with $a'=a/3$.
Cardioid Involute is a mirror-image cardioid with $a'=3a$.