Condition that 2 curves $$y^2=4 a x, x y=c^2$$ cut orthogonally is

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

Two particles $$P$$ and $$Q$$ located at the points $$P\left(t, t^3-16 t-3\right), Q\left(t+1, t^3-6 t-6\right)$$ are moving in a plane, the minimum distance between the points in their motion is

If $$x^3-2 x^2 y^2+5 x+y-5=0$$, then at $$(\mathrm{l}, \mathrm{l}), y^{\prime \prime}(\mathrm{l})=$$