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If any tangent to the ellipse `(x^(2))/(16) + (y^(2))/(9) = 1` intercepts equal lengths l on the both axis, then l =A. `3`B. `4`C. `sqrt(5)`D. None of these |
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Answer» Correct Answer - B The equation of any tangent of the given ellipse is `x/4 cos theta + y/3 sin theta = 1` The tangent meet `x`-axis at `A ((4)/(cos theta) ,0)` and `y`-axis at `B(0,(3)/(sintheta))` Given `(4)/(costheta) = l` and `(3)/(sintheta) = l` `rArr cos^(2)theta + sin^(2) theta = (16)/(l^(2)) + (9)/(l^(2)) rArr l = 5` |
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