Question:
Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (x, y) 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.