the shortest distance between the line `y-x=1` and the curve `x=y^(2)` is

Options

A. `sqrt3/4`
B. `(3sqrt2)/8`
C. `8/(3sqrt2)`
D. `4/sqrt3`

Answer

B

Explanation

Let `P(t^(2), t)` be point on the curve `x-=y^(2)` and S be the distance between P and the line `y-x-1=0`. Then, `S=|(t-t^(2)-1)/(sqrt(1+1))|=(t^(2)-t+1)/(sqrt2)=1/sqrt2{(t-1/2)^(2)+(sqrt3/2)^(2)}`
Clearly, S is minimum when`t=1/2`
For this value of t, we get