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Question

The shortest distance between the line y=x and the curve y2=x2 is:

A
1142
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B
742
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C
78
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D
2
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Solution

The correct option is B 742
Let PQ be the shortest distance between the line y=x and the curve y2=x2.

Slope of the line y=x is 1.
dydx at point P will be 1 as both are parallel.
Differentiating the curve y2=x2 w.r.t. x, we get
2yy=1
y=12y=12α=1
P=(94,12)
Minimum diatance is given by,
PQ=∣ ∣ ∣ ∣94122∣ ∣ ∣ ∣
=742

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