Concyclic points on ellipse

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

If alpha,beta,gamma,delta be eccentric angles ofthe four concyclic points ofthe ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then alpha+beta+gamma+delta=(A)(2n+1)(pi)/(2) (B) (2n-1)pi(C)2n pi(D)n pi

Concyclic points on hyperbola

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.

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.

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.

In the adjoining figure A, B, C, D are the concyclic points. The value of 'x' is :

Derive an equation to find distance of a point on ellipse to the focus of ellipse.