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Tuesday, March 28, 2017

Equation of Normal

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
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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