The area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is

If the tangent at a point on the ellipse $\frac{x^2}{27} + \frac{y^2}{3} = 1$ meets the coordinate axes at $A$ and $B,$ and $O$ is the origin,then the minimum area (in sq. units) of the triangle $OAB$ is

Let $P$ be a variable point on the ellipse $x^2 + 3y^2 = 3$. Then the maximum perpendicular distance of $P$ from the line $x - y = 10$ is (in $\sqrt{2}$)

Let $P$ be any point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. If $S_1$ and $S_2$ are its foci,then the maximum area of $\Delta PS_1S_2$ is (in square units):

The centre of an ellipse is $C$,$PN$ is any ordinate,and $A$,$A'$ are the end points of the major axis. Then the value of $\frac{PN^2}{AN \cdot A'N}$ is

Find the equation of the ellipse whose foci are $(\pm 2, 0)$ and eccentricity is $1/2$.