Position of Point Relative to Circle

Rarely Tested
For circle $$S: x^2 + y^2 + 2gx + 2fy + c = 0$$ and point $$P(x_1,y_1)$$:
- $$S(x_1,y_1) = 0$$ ⇒ on circle
- $$S(x_1,y_1) \lt 0$$ ⇒ inside circle
- $$S(x_1,y_1) \gt 0$$ ⇒ outside circle
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