Let P be a point on the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ and the line through P parallel to the Y-axis meets the circle x² + y² = 9 at Q, where P, Q are on the same side of the X-axis. If R is a point on PQ such that $${{PR} \over {RQ}} = {1 \over 2}$$, then the locus of R is

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