Area of ellipse `x^2/a^2 + y^2/b^2 = 1, a > b` is :

A normal inclined at 45^@ to the axis of the ellipse x^2 /a^2 + y^2 / b^2 = 1 is drawn. It meets the x-axis & the y-axis in P & Q respectively. If C is the centre of the ellipse, show that the area of triangle CPQ is (a^2 - b^2)^2/(2(a^2 +b^2)) sq units

A parabola is drawn whose focus is one of the foci of the ellipse x^2/a^2 + y^2/b^2 = 1 (where a>b) and whose directrix passes through the other focus and perpendicular to the major axes of the ellipse. Then the eccentricity of the ellipse for which the length of latus-rectum of the ellipse and the parabola are same is

Find the area bounded by the ellipse x^2/a^2 + y^2/b^2 = 1 and the ordinates x=0 and x=ae , where b^2 = a^2 (1-e^2) and e<1 .

Find the area of the smaller region bounded by the ellipse x^2/a^2 + y^2/b^2 = 1 and the straight line x/a + y/b = 1 (using integration)

Triangle AOB is in the first quadrant of the ellipse x^2/a^2+y^2/b^2=1 where OA = a and OB = b. Find the area enclosed between the chord AB and the arc AB of the ellipse.

If straight line lx + my + n=0 is a tangent of the ellipse x^2/a^2+y^2/b^2 = 1, then prove that a^2 l^2+ b^2 m^2 = n^2.

Find the maximum area of an isosceles triangle inscribed in the ellipse x^2/a^2 + y^2/b^2 = 1 with its vertex at one end of the major axis.

The eccentricity of the ellipse x^2/a^2+y^2/b^2=1 , if its latus rectum is half of its minor axis, is :

The locus of the foot of the perpendicular from the centre of the ellipse x^2/a^2+y^2/b^2=1 on any tangent is given by (x^2 + y^2)^2 = lx^2+my^2 , where: