A) \[l{{a}^{2}}+n{{b}^{2}}=0\]
B) \[l{{a}^{2}}=n{{b}^{2}}\]
C) \[2l{{a}^{2}}=n{{b}^{2}}\]
D) None of these
Correct Answer: B
Solution :
Let\[y={{m}_{1}}x\]and\[y={{m}_{2}}x\]be the lines represented by\[l{{x}^{2}}+2mxy+n{{y}^{2}}=0\], then \[{{m}_{1}}{{m}_{2}}=\frac{1}{n}\] ... (i) But\[y={{m}_{1}}x\]and\[y={{m}_{2}}x\]are conjugate diameters of the hyperbola. \[\therefore \] \[{{m}_{1}}{{m}_{2}}=\frac{{{b}^{2}}}{{{a}^{2}}}\] ... (ii) From Eqs. (i) and (ii), we get \[\frac{l}{n}=\frac{{{b}^{2}}}{{{a}^{2}}}\Rightarrow l{{a}^{2}}=n{{b}^{2}}\]
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