The coordinates of points P(x, y) lying in the first quadrant on the ellipsex2/8 + y2/18 = 1 so that the area of the triangle formed by the tangent at Pand the coordinate axes is the smallest, are given by

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Any point on the ellipse is given by                                          Hence the equation of the tangent at  is                   Therefore, the tangent cuts the coordinate axes at the points                              Thus the area of the triangle formed by this tangent and the coordinate axes is                                                                               But cosec 2&theta; is smallest when &theta; = &pi;/4. Therefore A is smallest when &theta; = &pi;/4. Hence the required points is

The Coordinates Of Points P(x, y) Lying In The First Quadrant On The Ellipsex2/8 + y2/18 = 1 So That The Area Of The Triangle Formed By The Tangent At Pand The Coordinate Axes Is The Smallest, Are Given By

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