First slide

Hyperbola in conic sections

Question

Which of the following pairs may represent the eccentricities of two conjugate hyperbolas, for all $α \in (0, π / 2) ?$

Moderate

A

$\sin θ, \cos θ$
B

$\tan θ, \cot θ$
C

$\sec θ, cosec θ$
D

$1 + \sin θ, 1 + \cos θ$

Solution

If e₁ and e₂are the eccentricities of two conjugate hyperbolas,
then $\frac{1}{e_{1}^{2}} + \frac{1}{e_{2}^{2}} = 1$
Therefore, $e_{1} = \sec θ and e_{2} = cosec θ$ .

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