Solution :
The equation of the two curves are
xy = 6 …….(i)
and, x2y = 12 …………(ii)
from (i) , we obtain y = 6x. Putting this value of y in (ii), we obtain
x2 (6x) = 12 ⟹ 6x = 12
⟹ x = 2
Putting x = 2 in (i) or (ii), we get y = 3.
Thus, the two curves intersect at P(2, 3).
Differentiating (i) with respect to x, we get
xdydx + y = 0 ⟹ dydx = −yx
⟹ m1 = (dydx)(2,3) = −32
Differentiating (ii) with respect to x, we get
x2 dydx + 2xy = 0 ⟹ dydx = −2yx
⟹ m2 = (dydx)(2,3) = -3
Let θ be the angle, then angle between angle between two curves
tanθ = m1–m21+m1m2 = 311
θ = tan−1(3/11)
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