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
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 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
$\frac{b}{{a - 2b}}$
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