If the points of intersections of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$ and the
circle x² + y² = 4b, b > 4 lie on the curve y² = 3x², then b is equal to :

If the curve x² + 2y² = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies :

Which of the following points lies on the locus of the foot of perpedicular drawn upon any tangent to the ellipse,
$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$
from any of its foci?