The equation of the normal to the curve y = x(2 - x) at the point (2, 0) is

x - 2y = 2 x - 2y + 2 = 0 2x + y = 4 2x + y - 4 = 0

x - 2y = 2

The equation of the curve is $y=x(2-x)$ or, $y=2 x-x^2$ $\Rightarrow \frac{d y}{d x}=2-2 x \Rightarrow\left(\frac{d y}{d x}\right)_{(2,0)}=2-2 \times 2=-2$ So, the equation of the normal at (2, 0) is $y-0=-\frac{1}{-2}(x-2)$  or,  $2 y=x-2$