The equation of normal to the circle (x – 1)2 + (y – 2)2 = 4 which is at a maximum distance from (–1,

Engineering

Mathematics

Length of Perpendicular

A Circle

Tangent and Normal to Circle

Question

The equation of normal to the circle (x – 1)² + (y – 2)² = 4 which is at a maximum distance from (–1, –1) is

3x + 2y = 7

x + 2y = 5

2x + 3y = 8

2x + y = 4

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Slope of line joining (– 1, – 1) and (1, 2) = $\frac{3}{2}$

⇒ Slope of normal = $- \frac{2}{3}$

⇒ Equation of normal is (y – 2) = $- \frac{2}{3}$ (x – 1)

⇒ 2x + 3y = 8.