Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. Let e' and l' respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If $${e^2} = {{11} \over {14}}l$$ and $${\left( {e'} \right)^2} = {{11} \over 8}l'$$, then the value of $$77a + 44b$$ 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 :

Let the eccentricity of the hyperbola $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be $$\sqrt {{5 \over 2}} $$ and length of its latus rectum be $$6\sqrt 2 $$. If $$y = 2x + c$$ is a tangent to the hyperbola H, then the value of c² is equal to

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