Question

Prove that the area bounded by the circle `x^2+y^2=a^2` and the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` is equal to the area of another ellipse having semi-axis `a-b` and `b ,a > b` .

Answer 1

Area bounded by the given circle and ellipse
= Area of circle -Area of ellipse
`=pia^(2)-piab=pia(a-b)`
= Area of ellipse having semi-axis a-b and b