Question

Find the equation of the circle passing through the point (2, 1) and touching the line x + 2y – 1 = 0 at the point (3, – 1).

Answer 1

Equation of circle is 

(x – 3)² + (y + 1)² + λ(x + 2y – 1) = 0 

Since it passes through the point (2, 1)

1 + 4 + λ (2 + 2 – 1) = 0 

⇒ λ = – 5/3 

∴ circle is 

(x – 3)² + (y + 1)² - 5/3(x + 2y - 1) = 0

⇒ 3x² + 3y² – 23x – 4y + 35 = 0