**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.