Let PQ be a focal chord of the parabola y^{2} = 4x such that it subtends an angle of $${\pi \over 2}$$ at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, $${a^2} > {b^2}$$. If e is the eccentricity of the ellipse E, then the value of $${1 \over {{e^2}}}$$ is equal to :

If vertex of a parabola is (2, $$-$$1) and the equation of its directrix is 4x $$-$$ 3y = 21, then the length of its latus rectum is :

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $$3x + y - 29 = 0$$, is $${x^2} + a{y^2} + bxy + cx + dy + k = 0$$, then $$a + b + c + d + k$$ is equal to :

Let the normal at the point on the parabola y^{2} = 6x pass through the point (5, $$-$$8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :