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

The eccentricity of the curve represented by $x=3(\cos t+\sin t), y=4(\cos t-\sin t)$ is

The foci of the conic $25 x^2+16 y^2-150 x=175$ are

AOB is the positive quadrant of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ in which $\mathrm{OA}=5, \mathrm{OB}=3$. The area between the arc AB and the chord AB of the ellipse in sq. units is