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Question

If the ellipse x24+y2=1 meets the ellipse x2+y2a2=1 in four distinct points and a=b2āˆ’5b+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>1a>1 or a<1.
For a<1
b25b+7<1b25b+8<0(b5/2)2+74<0
Which is not possible

For a>1
b25 b+7>1
b25 b+6>0
b(,2)(3,)
b doesn't lie on [2,3].

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