Coordinate Geometry: JEE Main 2022 Mathematics question

Let a circle C touch the lines ${L_1}:4x - 3y + {K_1} = 0$ and ${L_2} = 4x - 3y + {K_2} = 0$, ${K_1},{K_2} \in R$. If a line passing through the centre of the circle C intersects L₁ at $( - 1,2)$ and L₂ at $(3, - 6)$, then the equation of the circle C is :