Find the maximum area of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` which touches the line `y=3x+2.`

Find the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

Find the maximum distance of any normal of the ellipse x^2/a^2 + y^2/b^2=1 from its centre,

Find the length of Latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 .

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

Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the positive end of the latus rectum.

If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then find the maximum area of rectangle inscribed in the ellipse.

A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 in which O A=a ,O B=b . Then find the area between the arc A B and the chord A B of the ellipse.

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with AA' as the major axis. Find the maximum area of triangle A P A '

The area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 is equal to