Prove that for the curves \( a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c= \) 0 , at point \( p\left(x_...

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Prove that for the curves \( a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c= \) 0 , at point \( p\left(x_{1}, y_{1}\right) \), tangent is \( a x x_{1}+b y y_{1}+h\left(x y_{1}+x_{1} y\right)+ \) \( g\left(x+x_{1}\right)+f\left(y+y_{1}\right)+c=0 \)
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