Tangents drawn from the point  to the circle  touch the circle at the points and . The circumcircle of the  cuts the director circle of ellipse  orthogonally. Then the value of   is

(9)

Center of the given circle is

The circumcircle of  will circumscribe the quadrilateral also, hence one of the diameters must be

 Equation of circumcircle of  will be

    (1)

Director circle of given ellipse will be

         (2)

 From (1) and (2), by applying condition of orthogonality, we get

Hence