Show that the straight line joining two variable points on an ellipse, whose eccentric angles differ by a constant, touch a concentric ellipse.

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

If the eccentric angles of two points P and Q on the ellipse x^2/28+y^2/7=1 whose centre is C differ by a right angle then the area of Delta CPQ is

Show that the sum of the eccentric angles of any four concyclic points on an ellipse is equal to an even multiple of pi .

Show that the area of triangle inscribed in an ellipse bears a constant ratio to the area of thetriangle formed by joining points on the auxiliary circle corresponding to the vertices of the firsttriangle.

Show that the locus of the middle points of chord of an ellipse which paas through a fixed point, is another ellipse

If the angle between the straight lines joining foci and the ends of minor axis of the ellipse x^2/a^2+y^2/b^2=1 is pi/2 then the eccentricity is

Find the equation of the ellipse whose eccentricity is 1/2 and whose foci are at the points (pm2, 0) .

If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricity is 5/6 then the equation of the ellipse is

Area of the triangle formed by the tangents at the point on the ellipse x^2/a^2+y^2/b^2=1 whose eccentric angles are alpha,beta,gamma is

The parametric coordinates of a point on the ellipse, whose foci are (-3, 0) and (9, 0) and eccentricity (1)/(3) , are