WBJEE · Maths · Hyperbola
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 & Solution
Correct Answer
(A) 8: 1
Step-by-step Solution
Detailed explanation
Given equation of ellipses is \(x^{2}+9 y^{2}=9\) \(\Rightarrow \quad \frac{x^{2}}{9}+\frac{y^{2}}{1}=1\) Here, \(a=3, b=1\) \(c=\sqrt{(3)^{2}-(1)^{2}}=\sqrt{8}\) \(\therefore\) Eccentricity of ellipse, \(e=\frac{c}{a}\) \(e=\frac{\sqrt{8}}{3}\) \(\therefore\) Eccentricity of…
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