B is an extremity of the minor axis of an ellipse whose foci are S and S'. If $$\angle SBS'$$ is a right angle, then the eccentricity of the ellipse is

Tangents are drawn to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$ at the ends of both latusrectum. The area of the quadrilateral, so formed is

The line y = x + $$\lambda$$ is tangent to the ellipse 2x² + 3y² = 1. Then, $$\lambda$$ is

The equation of auxiliary circle of the ellipse $$16{x^2} + 25{y^2} + 32x - 100y = 284$$ is