The correct option is B tan−1 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=dydx⇒dydx=12y and dydx=2x⇒(dydx)(1,1)=12 and (dydx)(1, 1)=2⇒m1=12 and m2=2tan θ=(m1−m21+m1m2∣∣=(12−21+12×2∣∣
∣∣=(−322∣∣
∣∣=34⇒θ=tan−1(34)∴The acute angle between the curves is tan−1(34).