QJEEM19Ma77a3: JEE Main 2019 Mathematics - Class 12 JEEM19Ma77a3 Solution: The shortest distance between the point   ( 3 2 , 0 ) …

Question

Verified Solution • 2025–26 Session moderate

The shortest distance between the point

(\frac{3}{2}, 0)

and the curve y =

\sqrt{x}

, (x > 0), is -

Accepted Answer

Let points

(\frac{3}{2}, 0), (t^{2}, t), t > 0

Distance =

\sqrt{t^{2} + {(t^{2} - \frac{3}{2})}^{2}}

=

\sqrt{t^{4} - 2 t^{2} + \frac{9}{4}} = \sqrt{{(t^{2} - 1)}^{2} + \frac{5}{4}}

So minimum distance is

\sqrt{\frac{5}{4}} = \frac{\sqrt{5}}{2}

QJEEM19Ma77a3: JEE Main 2019 Mathematics - Class 12 JEEM19Ma77a3 Solution: The shortest distance between the point&nbsp;&nbsp; ( 3 2 , 0 ) …