The curve y = f x in the first quadrant is such that the y -intercept of the tangent drawn at any point P is equal to twice the ordinate of P . If y = f x passes through Q 2,3 , then the equation of the curve is

Step-by-step solution

General equation of the tangent at P x , y is Y - y = m X - x ∴ y -intercept is y - m x p u t   X = 0 ⇒ y - m x = 2 y ⇒ m x = - y or m = d y d x = - y x ⇒ d y y = - d x x On integrating, we get, ln y = - ln x + ln c ⇒ x y = c As it passes through 2,3 ⇒ c = 6 ⇒ y = f x   i s   x y = 6