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Question

The shortest distance between line yx=1 and curve x=y2 is

A
34
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B
328
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C
832
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D
43
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Solution

The correct option is C 328
Let P=(y2,y) be a point on the curve.
The perpendicular distance from P to xy+1=0 is |y2y+1|2
Now, the discriminant for the expression y2y+1 is negative and the co-efficient of y2 is positive. Hence, the expression y2y+1 is always positive.
For the minimum value of distance, y=12.
Hence,
Minimum distance =342=328

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