The focal distances of the point $$\left(\frac{4}{\sqrt{5}}, \frac{3}{\sqrt{5}}\right)$$ on the ellipse $$\frac{x^2}{4}+\frac{y^2}{9}=1$$ are

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

A point moves so that the sum of its distances from $$(a e, 0)$$ and $$(-a e, 0)$$ is $$2 a$$, then the equation to its locus, where $$b^2=a^2\left(1-e^2\right)$$ is