Question

Find the equation of circle passing through the points A(1, 1) & B(2, 2) and whose radius is 1.

Answer 1

Equation of AB is x – y = 0 

∴ equation of circle is 

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

or x² + y² + (λ – 3)x – (λ + 3)y + 4 = 0

or (λ – 3)² + (λ + 3)² – 16 = 4. 

or 2λ² = 2 

or λ = ± 1 

∴ equation of circle is 

x² + y² – 2x – 4y + 4 = 0 & x² + y² – 4x – 2y + 4 = 0