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Question

The shortest distance between the line yx=1 and the curve x=y2 is : 
  1. 325
  2. 34
  3. 328
  4. 238


Solution

The correct option is C 328
Let (a2,a) be the point of shortest distance on x=y2. Then distance between (a2,a) and line xy+1=0 is given by
D=a2a+12=12[(a12)2+34]
It is min when a=12 and Dmin=342=328
 

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