The area enclosed by the ellipse $4x^2 + 9y^2 = 1$ is . . . . . . sq. units.

The angle between the pair of tangents drawn from the point $(1, 2)$ to the ellipse $3x^2 + 2y^2 = 5$ is:

The eccentricity of the ellipse with minor axis $2b$,if the line segment joining the foci subtends an angle $2\alpha$ at the upper vertex,is equal to

The equation of the ellipse referred to its axes as the axes of coordinates with latus rectum of length $4$ and distance between foci $4 \sqrt{2}$ is-

The eccentricity of the ellipse $25x^2 + 16y^2 = 400$ is

If the chords of contact of tangents drawn from two points $(x_1, y_1)$ and $(x_2, y_2)$ to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are at right angles,then $\frac{x_1 x_2}{y_1 y_2} = \dots$