A tangent is drawn to the curve y = f(x) at p(x,y) cuts the x-axis and y -axis at A - Maths - Application of Integrals

Question

A tangent is drawn to the curve y = f(x) at p(x,y) cuts the
x-axis and y -axis at A and B respectively such taht BP= AP =3 :1 ,
given taht f(1) = 1 then show that curve passes through (2,1/8)

Ayushi · Answer

Equation of the tangent is
(Y − y)dx = dy (X x)

Given BP/AP=3/1

⇒ dx/x= - dy/3y

⇒dx/x+ dy/3y= 0

⇒ ln x =-1/3 lny- ln c

⇒ lnx^3 = − (ln cy)
⇒1/x^3=cy
= Given f(1) = 1 ⇒ c = 1
∴ y=1/x^3

therefore, (2,1/8) satisfies the curve

(By Ayushi;-))

A tangent is drawn to the curve y = f(x) at p(x,y) cuts the x-axis and y -axis at A and B respectively such taht BP= AP =3 :1 , given taht f(1) = 1 then show that curve passes through (2,1/8).