A) \[\frac{4}{\sqrt{3}}\]
B) \[\frac{\sqrt{3}}{4}\]
C) \[\frac{3\sqrt{2}}{8}\]
D) \[\frac{8}{3\sqrt{2}}\]
Correct Answer: C
Solution :
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
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