If the ellipse x24+y2=1 meets the ellipse x2+y2a2=1 in four distinct points and a=b2ā5b+7, then b does not lie in
A
(−∞,2)∪(3,∞)
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B
[4,5]
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C
[2,3]
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D
(−∞,0)
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Solution
The correct option is C[2,3] For the two ellipses to intersect in 4 distinct points, a2>1⇒a>1 or a<−1.
For a<−1 b2−5b+7<−1⇒b2−5b+8<0⇒(b−5/2)2+74<0
Which is not possible
For a>1 ⇒b2−5b+7>1 ⇒b2−5b+6>0 ⇒b∈(−∞,2)∪(3,∞) ∴b doesn't lie on [2,3].