If the normal drawn at a point $$P$$ on the curve $$3 y=6 x-5 x^3$$ passes through $$(0,0)$$, then the positive integral value of the abscissa of the point $$P$$ is

The line joining the points $$(0,3)$$ and $$(5,-2)$$ is a tangent to the curve $$y=\frac{c}{x+1}$$, then $$c=$$

If $$a, b>0$$, then minimum value of $$y=\frac{b^2}{a-x}+\frac{a^2}{x}, 0< x< a$$ is

The point on the curve $$y=x^2+4 x+3$$ which is closest to the line $$y=3 x+2$$ is