question_answer

The line \[lx+my+n=0\] will be a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if               [MP PET 2001]

A)            \[{{a}^{2}}{{l}^{2}}+{{b}^{2}}{{m}^{2}}={{n}^{2}}\]                     

B)            \[{{a}^{2}}{{l}^{2}}-{{b}^{2}}{{m}^{2}}={{n}^{2}}\]

C)            \[a{{m}^{2}}-{{b}^{2}}{{n}^{2}}={{a}^{2}}{{l}^{2}}\]                    

D)            None of these