COMEDK · Maths · 15. Hyperbola
If the distance between the foci and the distance between the directrices of the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) are in the ratio \(3: 2\), then \(a: b\) is
- A \(2: 1\)
- B \(1: 2\)
- C \(\sqrt{3}: \sqrt{2}\)
- D \(\sqrt{2}: 1\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2}: 1\)
Step-by-step Solution
Detailed explanation
Equation of hyperbola is \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) Distance between foci \(=2 a e\) and distance between directrices \(=\frac{2 a}{e}\) According to question, we have \(\frac{2 a e}{2 a / e}=\frac{3}{2}\)…
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