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Question

The shortest distance between the line xy=1 and the curve x2=2y is :

A
12
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B
0
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C
122
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D
12
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Solution

The correct option is C 122
Shortest distance must be along common normal


m1 (slope of line xy=1)=1
slope of perpendicular line =1
Slope of tangent line at (h,h22) is
m2=2x2=xm2=h
slope of normal =1h
So, 1h=1h=1
so point is (1,12)
D=∣ ∣ ∣11211+1∣ ∣ ∣=122

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