Q. 305.0( 1 Vote )

# Find the equation

Slope of tangent is given as Slope of tangent of a curve y = f(x) is given by   Integrate Using partial fraction for   Equating numerator

A(x + 1) + Bx = 1

Put x = 0

A = 1

Put x = -1

B = -1

Hence Hence equation (a) becomes  log(y – 1) = logx – log(x + 1) + c …(b)

Now it is given that the curve is passing through (1, 0)

Hence (1, 0) will satisfy the curve equation (b)

Putting values x = 1 and y = 0 in (b)

If we put y = 0 in (b) we get log (-1) which is not defined hence we must simplify further equation (b)

log (y – 1) – log x = – log (x + 1) + c

Using log a – log b = log   Using log a + log b = log ab Take the constant c as log c so that we don’t have any undefined terms in our equation (Why only log c and not any other term because taking log c completely eliminates the log terms so we don’t have to worry about the undefined terms appearing in our equation) Eliminating log Now substitute x = 1 and y = 0 c = -2

Put back c = -2 in (c) Hence the equation of curve is (y – 1)(x + 1) = -2x

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