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Question:

Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is 2yx^2. if the curve passes through the centre of the circle x^2 + y^2 - 2x - 2y = 0, then its equation is:

x log_e|y| = 2(x-1)

x^2 log_e|y| = -2(x-1)

x log_e|y| = -2(x-1)

x log_e|y| = x-1

Solution:

Correct option is A. x log_e|y| = 2(x-1)
given dydx = 2yx^2
⇒∫dy2y = ∫dxx^2
⇒12ℓ n|y| = - 1x + c
passes through centre (1, 1)⇒ c = 1
x ℓ n|y| = 2 (x-1)