The shortest distance between the point `(3/2,0)` and the curve `y=sqrtx,(xgt0)`, is `(sqrtk)/2`. The value of k is ___________.

Answer

5

Explanation

The point located nearest to the given point must be the point common to the parabola and the normal passing through `(3/2,0)`.
`(t/2)/((t^(2))/4-3/2)=-t`
`(2t)/(t^(2)-6)+t=0`
`t(2/(t^(2)-6)+1)=0`
`t^(2)-6=-2`
`t^(2)=4`
`t=2` `(tgt0)`
Point (1,1)
Distance `=sqrt((1-3/2)^(2)+1)=(sqrt5)/2`