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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

4

B

5

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of tangent is `y=4x+-sqrt(16a^(2)+b^(2))` this normal passes through `(-2,0)`
`implies 0=-8+-sqrt(16a^(2)+b^(2)),264=16a^(2)+b^(2)`
Giving `AMgeGM`
`(16a^(2)+b^(2))/2 ge sqrt(16a^(2)b^(2))`
`64/2ge sqrt(16a^(2)b^(2))`
`4able32`
`able8`
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