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

The number of those tangents to the curve $$y^2-2 x^3-4 y+8=0$$ which pass through the point $$(1,2)$$ is