Find the equation of the curve through the point (1, 0)

Question:

 Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (xy) is (y – 1)/ (x2 + x)

Solution:

Given that the slope of the tangent to the curve at (x, y) is

As, the line is passing through the point (1, 0), then (0 – 1) (1 + 1) = c(1) ⇒ c = 2

Thus, the required solution is (y – 1) (x + 1) = 2x.

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