Two poles, A B of length a metres and C D of length a+b(b \neq a) metres are erected at the same horizontal level with bases at \mathrm{B}$ and $\mathrm{D}. If \mathrm{BD}=x and \tan \angle \mathrm{ACB}=\frac{1}{2}, then :
Option: 1 x^{2}-2 \mathrm{a} x+\mathrm{a}(\mathrm{a}+\mathrm{b})=0
Option: 2 x^{2}+2(\mathrm{a}+2 \mathrm{~b}) x-\mathrm{b}(\mathrm{a}+\mathrm{b})=0
Option: 3 x^{2}+2(\mathrm{a}+2 \mathrm{~b}) x+\mathrm{a}(\mathrm{a}+\mathrm{b})=0
Option: 4 x^{2}-2 \mathrm{a} x+\mathrm{b}(\mathrm{a}+\mathrm{b})=0

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