Normal: The normal at any point P of the centre is the line which passes through P and is perpendicular to the tangent at P.
Equation of Normal:
i. The equation of the normal at p(x₁, y₁) of the circle
⇒ S = 0
⇒ x² + y² + 2gx + 2fy + c = 0 is (x - x₁) (y₁ + f) - (y - y₁) (x₁ + g) = 0
ii. The equation of the normal to the
circle x² + y² = r² at p(x₁, y₁) is xy₁ - yx₁ = 0.
iii. The line lx + my + n = 0 is a normal to the circle x² + y² + 2gx + 2fy + c = 0 if and only if gl + mf = n.
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