**Option : (B)**

If we consider the above figure as for getting it,their will be many points on the curve.

If the normal to the point B passes through the point(2,1) then point B will be the point having nearest distance from point (2,1).

Let B(x,y)

\(\frac{dy}{dx}\) = \(\frac{2}{y}\)

Slope at the point B is (2/y) and normal’s slope will be m=(–y/2) so by point slope formula.

⇒ (y - y_{1}) = m(x - x_{1}); (x_{1 }= 2,y_{1 }= 1)

⇒ (y - 1) = (-y/2)(x - 2)

⇒2y - 2 = -xy + 2y

⇒ xy = 2; y^{2} = 4x

⇒ from above to equations y^{3} = 8

⇒ y = 2 and x =1

So the nearest point is (1,2).