Smile is the shortest distance between two persons

Calculus Level 2

The shortest distance of the line $x-y-1=0$ from the curve $y=x^2$ is:

\frac 3{4\sqrt2}

3\sqrt2

\frac3{\sqrt2}

\frac 3{2\sqrt2}

1 solution

Manish Kumar Singh
Oct 15, 2015

Any point on the curve $y=x^2$ can be taken as $(t,t^2)$ , and its distance from the given line $x-y-1=0$ is given by:

d=sqrt[{(t^2) - t+1}^2]/2, or d^2=[{(t^2) - t+1}^2]/2; now for distance (d) to be minimum differentiate this expression with respect to t and put it equal to zero. it gives t=1/2. put this value back in to distance formula and you will get the answer.

One point you have forgotten then in distance formula there also comes modulus however it will not affect the answer as we are equating to 0

Nivedit Jain - 4 years, 2 months ago

Smile is the shortest distance between two persons

1 solution

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