Question

The shortest distance between line $y-x=1$ and curve $x=y^2$ is

• A. $\frac{4}{\sqrt{3}}$
• B. $\frac{\sqrt{3}}{4}$
• C. $\frac{3\sqrt{2}}{8}$
• D. $\frac{8}{3\sqrt{2}}$

Answer 1

Answer: (C)

The equation of the tangent to $x=y^2$ having slope
1 is $y=x+\frac{1}{4}$
Hence shortest distance $=\left|\frac{1-\frac{1}{4}}{\sqrt{2}}\right|$
$=\frac{3}{4\sqrt{2}}=\frac{3\sqrt{2}}{8}$ units