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If a tangent of slope 4 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 `ab` isA. 4B. 5C. 6D. 8 |
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Answer» Correct Answer - 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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