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

A
$x - 2 y = 2$
B
$x - 2 y + 2 = 0$
C
$2 x + y = 4$
D
$2 x + y - 4 = 0$

Solution:

The equation of the curve is

$\begin{array}{l} y = x (2 - x) or, y = 2 x - x^{2} \\ \Rightarrow \frac{d y}{d x} = 2 - 2 x \Rightarrow {(\frac{d y}{d x})}_{(2, 0)} = 2 - 2 \times 2 = - | 2 | \end{array}$

So, the equation of the normal at (2, 0) is

$y - 0 = - \frac{1}{- 2} (x - 2)$ or, $2 y = x - 2$

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

Solution:

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