The curve passing through P π 2 , π is such that for a tangent drawn to it at a point Q , the ratio of the y -intercept and the ordinate of Q is 1 : 2 . Then, the equation of the curve is

Step-by-step solution

General equation of the tangent at Q x , y is Y - y = m X - x Its y -intercept = y - m x ∴ y - m x y = 1 2 ⇒ 2 y - 2 m x = y ⇒ 2 m x = y ⇒ m = d y d x = y 2 x or ∫ d y y = ∫ d x 2 x ∴ ln ⁡ y = 1 2 ln ⁡ x + ln ⁡ C or y = C x As it passes through π 2 , π ⇒ C = 1 ∴ The curve is y = x