If the eccentricities of the hyperbolas \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and \[\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1\] be e and \[{{e}_{1}}\], then \[\frac{1}{{{e}^{2}}}+\frac{1}{e_{1}^{2}}=\] [MNR 1984; MP PET 1995; DCE 2000]

If the eccentricities of the hyperbolas \[\frac{{{x}^{2}}}{{{a}^{2}}}-

1.	If the eccentricities of the hyperbolas \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and \[\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1\] be e and \[{{e}_{1}}\], then \[\frac{1}{{{e}^{2}}}+\frac{1}{e_{1}^{2}}=\] [MNR 1984; MP PET 1995; DCE 2000]
A.	1
B.	2
C.	3
D.	None of these
Answer» B. 2

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If the eccentricities of the hyperbolas \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and \[\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1\] be e and \[{{e}_{1}}\], then \[\frac{1}{{{e}^{2}}}+\frac{1}{e_{1}^{2}}=\] [MNR 1984; MP PET 1995; DCE 2000]

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