The shortest distance between the line x−y=1 and the curve x2=2y is :
A
12
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B
0
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C
12√2
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D
1√2
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Solution
The correct option is C12√2 Shortest distance must be along common normal
m1(slope of line x−y=1)=1 ⇒ slope of perpendicular line =−1 Slope of tangent line at (h,h22) is m2=2x2=x⇒m2=h ⇒slope of normal =−1h So, −1h=−1⇒h=1 so point is (1,12) ⇒D=∣∣
∣
∣∣1−12−1√1+1∣∣
∣
∣∣=12√2