A surveyor describes the edge of a field by a curve of the family y = ax + b/x for x > 0, where a…

Step 1. Check the equation. $x^2\dfrac{2b}{x^3} + x\left(a - \dfrac{b}{x^2}\right) - ax - \dfrac{b}{x} = \dfrac{2b}{x} - \dfrac{b}{x} - \dfrac{b}{x} = 0$. The terms in $a$ also cancel, so the equation fits.

Step 2. The conditions. $a + b = 5$ and $a - b = 1$. Adding: $2a = 6$, so $a = 3$. Then $b = 2$.

Step 3. The value of $y$. $y(2) = 3 \times 2 + \dfrac{2}{2} = 7$.

Step 4. The curvature. $y'' = \dfrac{2b}{x^3} = \dfrac{4}{x^3}$. At $x = 2$ this is $\dfrac{4}{8} = 0.5$.