☼ Orthogonal Curves  :   If  the tangents of  both the curves at their point of  intersection are perpendicular to each other, then the both curves are called orthogonal curves.

↦ Two circles S : x²  + y² + 2g₁ x + 2f₁ y + c₁ = 0  &  S₂ : x² + y² + 2g₂x + 2f₂y + c₂ = 0  cut orthogonally, if

2g₁g₂+ 2f₁f₂ =  c₁+ c₂

↦ Let  S₁  =  0  &  and  S₂  =  0  be two intersecting circles. Then, the equation of  their common chord is  S₁ – S₂  =  0.

i.e.,  2 ( g₁ – g₂ )x  + 2 ( f₁ – f₂ )y  + ( c₁ – c₂ )  =  0.

☼ Points of  Intersection of  Two Curves  :   If  a line and a curve intersect or two curves intersect, then their points of  intersection may be obtained by solving their equations simultaneously.

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