The equation of the circle described on the chord 3 x ⁡ + y ⁡ + 5 = 0 of the circle x ⁡ 2 + y ⁡ 2 = 1 6 as the diameter is

Step-by-step solution

We know that the equation of the family of circle passing through the point of intersection of a circle S = 0 and a line L = 0 is S + λ L = 0 . Hence, the family of circle passing through points of intersection of given circle x 2 + y 2 - 16 = 0 and chord 3 x + y + 5 = 0 is ( x 2 + y 2 - 16 ) + λ 3 x + y + 5 = 0 ⇒ x 2 + y 2 + 3 λ x + λ y + 5 λ - 16 = 0 We know that, the centre of a circle x 2 + y 2 + 2 g x + 2 f y + c = 0 is - g ,   - f Hence, centre of the circle x 2 + y 2 + 3 &