Chord with Given Midpoint

Rarely Tested
Chord of circle $$S=0$$ with midpoint $$(x_1,y_1)$$:
$$T(x_1,y_1) = S(x_1,y_1)$$
i.e., $$xx_1 + yy_1 + g(x+x_1) + f(y+y_1) + c = x_1^2 + y_1^2 + 2gx_1 + 2fy_1 + c$$
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