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If a tangent of slope 2 of the ellipse (...

If a tangent of slope 2 of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` is normal to the circle `x^2+y^2+4x+1=0` , then the maximum value of `a b` is 4 (b) 2 (c) 1 (d) none of these

A

2

B

4

C

6

D

Can not be found

Text Solution

Verified by Experts

The correct Answer is:
B
A tangent of slope 2 is `y=2x pm sqrt(4a^(2)+b^(2))` this is normal to `x^(2)+y^(2)+4x+1=0` then
`0=-4pm sqrt 4a^(2)+b^(2)) rArr 4a^(2)+b^(2)=16`
Using `AM ge GM" " ab le 4`
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