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