Question

Find the equation of a circle which cuts the circle x² + y² – 6x +4y – 3 = 0 orthogonally and which passes though (3, 0) and touches the y-axis. 

Answer 1

When two circle intersects each other orthogonally then 2(g₁ g₂ + f₁ f₂) = c₁ + c₂. Hence by considering centre as (h, k) and using given condition we can solve problem

Let C(h, k) be the centre of required circle 

It is intersected by x² + y² – 6x + 4y – 3 = 0 , orthogonally; 

Required circle is x² + y² – 6x – 6y + 9 = 0