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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 = 2 x pm sqrt(4a^2 +b^2)` this is normal to `x^2 + y^2 + 4x +1 =0` then
`0= 4 pm sqrt(4a^2 +b^2) rArr 4a^2 +b^2 =16`
Using `AM ge GM ab le 4`
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