The point on the curve $$y^2=2(x-3)$$ at which the normal is parallel to the line $$y-2 x+1=0$$ is

For two events $$\mathrm{A}$$ and $$\mathrm{B}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{5}{6}, \mathrm{P}(\mathrm{A})=\frac{1}{6}, \mathrm{P}(\mathrm{B})=\frac{2}{3}$$, then $$\mathrm{A}$$ and $$\mathrm{B}$$ are

A rectangle of maximum area is inscribed in an ellipse $$\frac{x^2}{25}+\frac{y^2}{16}=1$$, then its dimensions are

The area bounded between the curve $$x^2=y$$ and the line $$y=4 x$$ is