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

The points of the ellipse 16x² + 9y² = 400 at which the ordinate decreases at the same rate at which the abscissa increases is/are given by