question_answer

The line \[lx+my+n=0\] will be a normal to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\] is _____.

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

B)  \[\frac{{{a}^{2}}}{{{l}^{2}}}+\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{2{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\]

C)  \[\frac{{{a}^{2}}}{{{l}^{2}}}+\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\]

D)  \[\frac{{{a}^{2}}}{{{l}^{2}}}-\frac{{{b}^{2}}}{{{m}^{2}}}=\frac{2{{({{a}^{2}}+{{b}^{2}})}^{2}}}{{{n}^{2}}}\]

E)  None of these