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Question

The acute angle between the curves y2=x and x2=y at (1, 1) is .

A
tan1 43
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B
tan1 34
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C
90°
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D
45°
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Solution

The correct option is B tan1 34
The given curves are y2=x and x2=y.
Let θ be the acute angle between the
given curves.
Let m1 and m2 be the slope of the given curves y2=x and x2=y at (1, 1)
Differentiating both sides w.r.t. x,
we get
2ydydx=1 and 2x=dydxdydx=12y and dydx=2x(dydx)(1,1)=12 and (dydx)(1, 1)=2m1=12 and m2=2tan θ=(m1m21+m1m2=(1221+12×2∣ ∣=(322∣ ∣=34θ=tan1(34)The acute angle between the curves is tan1(34).

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