AP EAMCET · Maths · Ellipse
If \(e\) and \(e^{\prime}\) are the eccentricities of the ellipse \(5 x^2+9 y^2=45\) and the hyperbola \(5 x^2-4 y^2=45\) respectively, then \(e e^{\prime}\) is equal to
- A \(1\)
- B \(4\)
- C \(5\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
Equation of ellipse is or \[ \begin{array}{r} 5 x^2+9 y^2=45 \\ \frac{x^2}{9}+\frac{y^2}{5}=1 \\ e=\sqrt{\frac{1-b^2}{a^2}}=\sqrt{\frac{1-5}{9}}=\frac{2}{3} \end{array} \] and equation of hyperbola is \[ 5 x^2-4 y^2=45 \] or…
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