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Q)

For the equation to represent the hyperbola $\large\frac{x^2}{9-\lambda}+\frac{y^2}{6-\lambda}$$=1$ what should be the value of $\lambda$?

$\begin{array}{1 1}(a)\;\lambda \in (6,9)\\(b)\;\lambda \in (4,3)\\(c)\;\lambda \in (3,9)\\(d)\;\lambda \in (2,4)\end{array}$

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A)
If $9-\lambda > 0$ & $6-\lambda < 0$ the equation will represent hyperbola hence
(i) $9-\lambda > 0$
$\lambda < 9$
(ii) $6-\lambda > 0$
$\lambda > 6$
Taking intersection of (i) & (ii)
$\lambda \in (6,9)$
Hence (a) is the correct answer.
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