A tangent to the curve, y = f x at P x , y meets x -axis at A and y -axis at B . If A P : B P = 1 : 3 and f 1 = 1 , then the curve also passes through the point

Step-by-step solution

Equation of tangent, Y − y = d y d x ( X − x ) A ( x − y d x d y , 0 )     ​ :     B ( 0 , y − x d y d x ) Given, A P : B P = 1 : 3 , Using section formula, we get y = y − x d y d x 4 ⇒ y − x d y d x = 4 y ⇒ d y y + 3 d x x = 0 By integrating w.r.t x , we get ln | y | + 3 ln | x | = ln c | y x 3 | = c ∵ f ( 1 ) = 1 ∴ c = 1 ⇒ | y x 3 | = 1 Hence, the curve passes throught the point 2 , 1 8