Question

Let the eccentricity of the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) be reciprocal to that of the ellipse \(x^{2}+9 y^{2}=9\), then the ratio \(a^{2}: b^{2}\) equals
(A) \(8: 1\)
(B) \(1: 8\)
(C) \(9: 1\)
(D) \(1: 9\)

Answer 1

Ans : (A)
Hint \(: 1+\frac{b^{2}}{a^{2}}=\frac{9}{8}\)
\(\Rightarrow \frac{b^{2}}{a^{2}}=\frac{1}{8}\)
\(\Rightarrow \frac{a^{2}}{b^{2}}=\frac{8}{1}\)

Answer 2

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