If x^2α+3+y^22-α=1 represents a hyperbola, then α lies in

Correct answer: (D) (-∞, -3)∪(2, ∞). For x^2α+3+y^22-α=1 to represent a hyperbola α+32-α 0 ⇒α∈-∞,-3∪2, ∞

Q100 / 160 · TS EAMCET 2021 (05 Aug Shift 1) · Mathematics

If $\frac{x^{2}}{α + 3} + \frac{y^{2}}{2 - α} = 1$ represents a hyperbola, then $α$ lies in

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

$(α + 3) (2 - α) < 0$

$\Rightarrow (α + 3) (α - 2) > 0$

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

Hence, the correct answer is option: 'D'.