Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of

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

P is the extremity of the latusrectum of ellipse $$3{x^2} + 4{y^2} = 48$$ in the first quadrant. The eccentric angle of P is

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