A stick of length $$r$$ units slides with its ends on coordinate axes. Then, the locus of the mid-point of the stick is a curve whose length is

The eccentric angle of a point on the ellipse $$x^2+3 y^2=6$$ lying at a distance of 2 units from its centre is

If $$\tan \theta_1, \tan \theta_2=\frac{-a^2}{b^2}$$, then the chord joining 2 points $$\theta_1$$ and $$\theta_2$$ one the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ will subtend a right angle at

In an ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentricity is