A) \[\frac{\sqrt{5}}{2}\]
B) \[2\sqrt{5}\]
C) \[\frac{\sqrt{5}}{4}\]
D) \[4\sqrt{5}\]
Correct Answer: A
Solution :
The straight line \[x+2y=1\]meets the coordinate axes at (1, 0) and (0, 1/2). Since \[\angle AOB={{90}^{o}}\] \[\therefore \]Equation of circle is \[(x-1)(x-0)+(y-0)\left( y-\frac{1}{2} \right)=0\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}-x-\frac{y}{2}=0\] Now, equation of tangent at origin to the given circle is \[2x+y=0\] Now, \[{{l}_{1}}=\frac{\left| 0+\frac{1}{2} \right|}{\sqrt{4+1}}=\frac{1}{2\sqrt{5}}\] Similarly,\[{{l}_{2}}=\frac{2}{\sqrt{5}}\] \[\therefore \]\[{{l}_{1}}+{{l}_{2}}=\frac{1}{2\sqrt{5}}+\frac{2}{\sqrt{5}}=\frac{\sqrt{5}}{2}\]You need to login to perform this action.
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