Let a circle \( C \) touch the lines \( L_{1}: 4 x-3 y+K_{1}=0 \) and \( L_{2}: 4 x-3 y+K_{2}=0,...

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Let a circle \( C \) touch the lines \( L_{1}: 4 x-3 y+K_{1}=0 \) and \( L_{2}: 4 x-3 y+K_{2}=0, K_{1}, K_{2} \in R \). If a line passing through the centre of the circle \( \mathrm{C} \) intersects \( L_{1} \) at \( (-1,2) \) and \( L_{2} \) at \( (3,-6) \), then the equation of the circle \( C \) is
(a) \( (x-1)^{2}+(y-2)^{2}=4 \)
(b) \( (x+1)^{2}+(y-2)^{2}=4 \)
(c) \( (x-1)^{2}+(y+2)^{2}=16 \)
(d) \( (x-1)^{2}+(y-2)^{2}=16 \)
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