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A tangent drawn to the curve y=f(x) at P...

A tangent drawn to the curve `y=f(x)` at `P(x,y)` cuts the x-axis and y-axis at `A` and `B` respectively such that `BP:AP=2:1`. Given that `f(1)=1`. Answer the question: Equation of curve is (A) `y=1/x` (B) `y=1/x^2` (C) `y=1/x^3` (D) none of these

A

equation of the curve is `x (dy)/(dx) - 3y = 0`

B

normal at (1,1) is `x + 3y = 4`

C

curve passes through `(2, 1//8)`

D

equation of the curve is `x (dy)/(dx) + 4y =0`

Text Solution

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The correct Answer is:
C
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