EXERCISE

Area of the greatest rectangle inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is

An ellipse has $OB$ as semi minor axes, $F$ and $F\text{'}$ its foci and the angle $FBF\text{'}$ is a right angle. Then the eccentricity of the ellipse is 

The eccentricity of the ellipse $(x-3{)}^2+(y-4{)}^2=\frac{y^2}{9}$ is

If the two tangents drawn from a point $P$ to the parabola $y^2=4x$ are at right angles then the locus of $P$ is

The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point 

The locus of a point whose distance from $(-2,0)$ is $\frac{2}{3}$ times its distance from the line $x=\frac{-9}{2}$ is

The values of $m$ for which the line $y=mx+2\sqrt{5}$ touches the hyperbola $16x^2-9y^2=144$ are the roots of $x^2-(a+b)x-4=0$, then the value of $(a+b)$ is

If the coordinates at one end of a diameter of the circle $x^2+y^2-8x-4y+c=0$ are $(11,2)$, the coordinates of the other end are