If x23−α+y22=1 represents an ellipse whose major axis is along the x−axis, then the range of α is
A
(1,∞)
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B
(−∞,1)
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C
(−∞,−1)
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D
(3,∞)
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Solution
The correct option is B(−∞,1) Given x23−α+y22=1 Comparing this with x2a2+y2b2=1 Then a2=3−α,b2=2 As a2>0, so 3−α>0⇒α<3⋯(1) Also, the major axis is along the x−axis, so a2>b2⇒3−α>2⇒α<1⋯(2) From (1) and (2), α∈(−∞,1)