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Question

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

(a) tan-1 43
(b) tan-1 34
(c) 90°
(d) 45°

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Solution

(b) tan-1 34

Given:y2=x ...1x2=y ...2Point=1, 1On differentiating (1) w.r.t. x, we get2y dydx=1dydx=12ym1=12On differentiating (2) w.r.t. x, we get2x = dydxm2=21=2Now,tan θ=m1-m21+m1m2=12-21+12×2=34θ=tan-1 34

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