The total number of tangents through the point (3, 5) that can be drawn to the ellipse 3x² + 5y² = 32 and 25x² + 9y² = 450 is

The line y = 2t² intersects the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ in real point if

The angle between the line joining the foci of an ellipse to one particular extremity of the minor axis is 90$$^\circ$$. The eccentricity of the ellipse is

S and T are the foci of an ellipse and B is an end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is