The shortest distance between line y – x = 1 and curve x = y2 is :
Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.
Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA
y – x = 1
y2 = x
\(2y\frac{{dy}}{{dx}} = 1\)
\(\frac{{dy}}{{dx}} = \frac{1}{{2y}} = 1\)
\(y = \frac{1}{2}\)
\(x = \frac{1}{4}\)
tangent at \(\left( {\frac{1}{4},\frac{1}{2}} \right)\)
\(\frac{1}{2}y = \frac{1}{2}\left( {x + \frac{1}{4}} \right)\)
\(y = x + \frac{1}{4}\)
\(y - x = \frac{1}{4}\)
distance \( = \left| {\frac{{1 - \frac{1}{4}}}{{\sqrt 2 }}} \right| = \frac{3}{{4\sqrt 2 }} = \frac{{3\sqrt 2 }}{8}\)