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The condition that the straight line \( l x+m y=n \) may
\( \mathrm{P} \) be a normal to the hyperbola \( b^{2} x^{2}-a^{2} y^{2}=a^{2} b^{2} \) is

W given by
(1) \( \frac{a^{2}}{l^{2}}-\frac{b^{2}}{m^{2}}=\frac{\left(a^{2}+b^{2}\right)^{2}}{n^{2}} \)
(2) \( \frac{l^{2}}{a^{2}}-\frac{m^{2}}{b^{2}}=\frac{\left(a^{2}+b^{2}\right)^{2}}{n^{2}} \)
(3) \( \frac{a^{2}}{l^{2}}+\frac{b^{2}}{m^{2}}=\frac{\left(a^{2}-b^{2}\right)^{2}}{n^{2}} \)
(4) \( \frac{l^{2}}{a^{2}}+\frac{m^{2}}{b^{2}}=\frac{\left(a^{2}-b^{2}\right)^{2}}{n^{2}} \)
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