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(D) : Distance between foci is three times the distance between its directrices.$2ae = 3 	imes \frac{2a}{e}$ $\Rightarrow e^2 = 3$ $\Rightarrow e = \

Vedclass · Accepted Answer

$A, C, B$

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(D) : Distance between foci is three times the distance between its directrices.$2ae = 3 	imes \frac{2a}{e}$ $\Rightarrow e^2 = 3$ $\Rightarrow e = \sqrt{3} \approx 1.732$$B$: The transverse axis is twice the conjugate axis.$2a = 2(2b)$ $\Rightarrow a = 2b$ $\Rightarrow b = \frac{a}{2}$.We know that $a^2e^2 = a^2 + b^2 = a^2 + \frac{a^2}{4} = \frac{5a^2}{4}$.$e^2 = \frac{5}{4} \Rightarrow e = \frac{\sqrt{5}}{2} \approx 1.118$$C$: Slopes of asymptotes are $m_1 = -1$ and $m_2 = 1$.Since $m_1 \cdot m_2 = -1$,it is a rectangular hyperbola.$e = \sqrt{2} \approx 1.414$Comparing the values: $1.732 > 1.414 > 1.118$.Thus,the descending order is $A, C, B$.

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