The area of the region enclosed by the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is . . . . . . square units. (in $\pi$)

The tangent to the ellipse $9x^2 + 16y^2 = 288$ making equal intercepts on the coordinate axes intersects the $X$-axis and the $Y$-axis at points $A$ and $B$ respectively. Then,the area of $\triangle OAB$ (where $O$ is the origin) is:

The ellipse having its foci $(0, \pm 1)$ and major axis of length $\sqrt{5}$ is

If the eccentricity of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, (a > b)$ is $e = 2/3$ and its focal chord is $3x + 2y - 6 = 0$, then the value of $a^2 + b^2$ is...

The eccentricity of the conic $36x^2 + 144y^2 - 36x - 96y - 119 = 0$ is

What is the equation of the chord of the ellipse $\frac{x^2}{36} + \frac{y^2}{9} = 1$ that is bisected at the point $(2, 1)$?