Let slope of the tangent line to a curve at any point P x , y be given by x y 2 + y x . If the curve intersects the line x + 2 y = 4 at x = - 2 , then the value of y , for which the point 3 , y lies on the curve, is :

Step-by-step solution

Given d y d x = x y 2 + y x x d y - y d x y 2 = x d x - d x y = x d x - x y = x 2 2 + c ∵ Curve intersects the line x + 2 y = 4 at x = - 2 ⇒ point of intersection is - 2 , 3 . ∴ Curve passes through - 2 , 3 . ⇒ 2 3 = 2 + c ⇒ c = - 4 3 ⇒ - x y = x 2 2 - 4 3 Now put 3 , y we get, ⇒ - 3 y = 19 6 ⇒ y = - 18 19