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)

Answer 1

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.