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

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x − 2y = 2 \text { Here }, y = x\left( 2 - x \right) = 2x - x^2 \Rightarrow dy/dx = 2 - 2x \text { Slope of the tangent }= \left( dy/dx \right)_\left( 2, 0 \right) = 2 - 4 = - 2 \text { Slope of the normal }, m=- 1/- 2=$\frac{1}{2}$ \text { Given }: \left( x_1 , y_1 \right) = \left( 2, 0 \right) \therefore \text { Equation of the normal } = y - y_1 = m\left( x - x_1 \right) \Rightarrow y - 0 = $\frac{1}{2}$\left( x - 2 \right) \Rightarrow 2y = x - 2 \Rightarrow x - 2y = 2

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