Area of the ellipse `x^2/a^2+y^2/b^2=1`

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

Number of points on the ellipse x^2/a^2+y^2/b^2=1 at which the normal to the ellipse passes through at least one of the foci of the ellipse is

If the ellipse x^2/a^(2)+y^2/b^(2)=1 is inscribed in a rectangle whose length to breadth ratio is 2 :1 then the area of the rectangle is

Determine the equation of the ellipse x^(2)/a^(2)+y^(2)/b^(2) = 1 such that it has the least area but contains the circle (x-1)^(2)+ y^(2) = 1 .