Equation of the ellipse whose axes of coordinates and which passes through the point $$(-3,1)$$ and has eccentricity $$\sqrt {{2 \over 5}} $$ is :

$${{{d^2}x} \over {d{y^2}}}$$ equals:

For $$x \in \left( {0,{{5\pi } \over 2}} \right),$$ define $$f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $$ Then $$f$$ has

The shortest distance between line $$y-x=1$$ and curve $$x = {y^2}$$ is