Question

The line 2x + 3y = 1 cuts the circle x² + y² = 4 at points A and B. Show that the equation of the circle described on AB as diameter is 13(x² + y²) − 4x − 6y − 50 = 0.

Answer 1

Let S≡ x² + y² − 4 = 0 and L ≡ 2x + 3y − 1 = 0. The required circle equation is

 The centre of the circle is

 Since AB is the diameter of S + λL = 0 and (λ) lies on L = 0, we have