If x 2 α + 3 + y 2 2 - α = 1 represents a hyperbola, then α lies in

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Question: Answered & Verified by Expert

If

\frac{x^{2}}{α + 3} + \frac{y^{2}}{2 - α} = 1

represents a hyperbola, then

α

lies in

MathematicsHyperbolaTS EAMCETTS EAMCET 2021 (05 Aug Shift 1)

Options:

A $(- 3, 2)$
B $(- 3, \infty)$
C $(- \infty, - 2)$
D $(- \infty, - 3) \cup (2, \infty)$

Solution:

1752 Upvotes Verified Answer

The correct answer is:

(- \infty, - 3) \cup (2, \infty)

For $\frac{x^{2}}{α + 3} + \frac{y^{2}}{2 - α} = 1$ to represent a hyperbola

$(α + 3) (2 - α) < 0$

$\Rightarrow (α + 3) (α - 2) > 0$

$\Rightarrow α \in (- \infty, - 3) \cup (2, \infty)$

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