Show that the tangents at the ends of conjugate diameters of the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` intersect on the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=2`.

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

The line lx+my=n is a normal to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1

Find the eccentricity of the ellipse x^(2)/(a^(2))+y^(2)/b^(2)=1 when a=5 and b=3.

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

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

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

Find the equation of the tangent to the ellipse (x^2)/a^2+(y^2)/(b^2) = 1 at (x_1y_1)

Triangles are formed by pairs of tangent drawn from any point on the ellipse a^(2)x^(2)+b^(2)y^(2)=(a^(2)+b^(2)) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 and the chord of contact. Show that the orthocentre of each such triangles lies triangle lies on the ellipse.