The equation of the normal to the curve y = x(2 - x) at the point (2, 0) is
Answer & explanation
Correct answer: option 1
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, $2 y=x-2$