If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is :

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points?

If the normal to the ellipse 3x² + 4y² = 12 at a point P on it is parallel to the line, 2x + y = 4 and the tangent to the ellipse at P passes through Q(4,4) then PQ is equal to :

The tangent and normal to the ellipse 3x² + 5y² = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is :