Ellipse

Let be an isosceles triangle inscribed in the ellipse
Let co-ordinate of be
Area of is





Put





Since for
Max. Area
sunits

For an ellipse, the eccentricity is given by: where is the semi-major axis and is the semi-minor axis. We are told that the length of the major axis is 3 times the length of the minor axis. Therefore: Substitute this into the formula for eccentricity: Thus, the correct answer is option (B)

The given equation represents an ellipse in standard form, which can be written as: For an ellipse, the area is given by the formula: where and are the semi-major and semi-minor axes of the ellipse. In this case, and (since the equation of the ellipse is ). Substituting these values into the area formula: Thus, the area of the region enclosed by the curve is sq units.