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The shortest distance between the line $y = x$ and the curve $y^2 = x - 2$ is:
(1) $2$
(2) $\frac{7}{8}$
(3) $\frac{7}{4\sqrt{2}}$
(4) $\frac{11}{4\sqrt{2}}$
Tangent to $y^2 = x - 2$ with slope 1: $y = x - \frac{7}{4}$. Distance from $y = x$: $\frac{7/4}{\sqrt{2}} = \frac{7}{4\sqrt{2}}$.
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