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

Prove that the sum of eccentric angles of four concylic points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is 2npi, where n in Z

If theta is the difference of the eccentric angles of two points on an ellipse, the tangents at which are at right angles. Prove that a b sintheta=d_1d_2 , where d_1,d_2 are the semi diameters parallel to the tangents at the points and a,b are the semi-axes of the ellipse.

Find the sum of the focal distances of any point on the ellipse 9x^2+16 y^2=144.

Find the sum of the focal distances of any point on the ellipse 9x^2+16 y^2=144.

If the eccentricity of an ellipse is 1/sqrt2 , then its latusrectum is equal to its

If alpha, beta, gamma be the eccentric angles of three points of an ellipse, the normals at which are concurrent, show that sin(alpha+beta) + sin (beta+gamma) + sin (gamma + alpha) = 0 .

If alpha and beta are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is (sinalpha+sinbeta)/("sin"(alpha+beta))

A circle and a parabola y^2=4a x intersect at four points. Show that the algebraic sum of the ordinates of the four points is zero. Also show that the line joining one pair of these four points is equally inclined to the axis.

Prove that product of parameters of four concyclic points on the hyperbola xy=c^(2) is 1. Also, prove that the mean of these four concyclic points bisects the distance between the centres of the hyperbola and the circle.

The sum of focal distances of any point on the ellipse 9x^(2) + 16y^(2) = 144 is