If \[a>2b>0\]then the positive value of m for which \[y=mx-b\sqrt{1+{{m}^{2}}}\]is a common tangent to \[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]and \[{{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}}\], is [IIT Screening 2002]

\[\frac{\sqrt{{{a}^{2}}-4{{b}^{2}}}}{2b}\]

\[\frac{2b}{\sqrt{{{a}^{2}}-4{{b}^{2}}}}\]

If \[a>2b>0\]then the positive value of m for which \[y=mx-b\sqrt{1+{{

1.	If \[a>2b>0\]then the positive value of m for which \[y=mx-b\sqrt{1+{{m}^{2}}}\]is a common tangent to \[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]and \[{{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}}\], is [IIT Screening 2002]
A.	\[\frac{2b}{\sqrt{{{a}^{2}}-4{{b}^{2}}}}\]
B.	\[\frac{\sqrt{{{a}^{2}}-4{{b}^{2}}}}{2b}\]
C.	\[\frac{2b}{a-2b}\]
D.	\[\frac{b}{a-2b}\]
Answer» B. \[\frac{\sqrt{{{a}^{2}}-4{{b}^{2}}}}{2b}\]

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If \[a>2b>0\]then the positive value of m for which \[y=mx-b\sqrt{1+{{m}^{2}}}\]is a common tangent to \[{{x}^{2}}+{{y}^{2}}={{b}^{2}}\]and \[{{(x-a)}^{2}}+{{y}^{2}}={{b}^{2}}\], is [IIT Screening 2002]

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