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Tangents, parallel to angle bisector of lines `lx+my+n=0` and `ax +by +c=0` are drawn to ellipse `(x^(2))/(36)+(y^(2))/(64)=1`, so as to generate a quadrilateral with vertices as points of intersection of these tangents and inscribing the ellipse. Then the maximum area of the quadrilateral is-A. `100`B. `200`C. `300`D. `400` |
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Answer» Correct Answer - B Any pair of angle bisectors of real and intersecting lines are perpendicular to each other. Hence the tangents which are obtained will be opposite pair wise parallel and adjacent pair wise perpendicular. Hence the quadrilaternal will be a rectangle. Also vertices of this rectangle will lie on the director circle of the ellipse, Which is Of all the rectangle that can be inscribed in this circle the maximum area is of the one which is a square having area 200. This square is easily observed when vertices lie on the co-ordinate axes. Ans.200` |
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