Show that the area of the ellipse `x^2/a^2+y^2/b^2=1` is always less than `4ab`. Also deduce the area formed by the ends of the latus recta.

Find the area of ellipse x^2/6+y^2/25=1 .

Find the area of the ellipse x^2/25+y^2/16=1 using integration.

The latus rectum of the ellipse 9x^2+16y^2=144 , is:

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

In the ellipse x^2/120+y^2/16=1 , show that the area of the triangle formed by : two foci and one end of minor axis is 8sqrt26 .

The length of the latus rectum of the ellipse 9x ^(2) + 4y ^(2) =1, is

Find the area bounded by the parabola y^2 = 4ax and its latus rectum.