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Find the shortest distance between the line `x - y +1 = 0` and the curve `y^2 = x.`A. `sqrt3/4`B. `(3sqrt2)/8`C. `8/(3sqrt2)`D. `4/sqrt3` |
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Answer» Correct Answer - B 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 |
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