Application of DerivativeHard

Question

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 = 3 : 1, given that f(1) = 1, then

Options

A.equation of curve is x - 3y = 0
B.normal at (1, 1) is x + 3y = 4
C.curve passes through (2, 1/8)
D.equation of curve is x + 3y = 0

Solution

     
Equation of the tangent is
Y - y = (X - x)
Given so that
⇒   + 3y = 0
⇒   ln x = - ln y - ln c ⇒ lnx3 = - (ln cy)
⇒   = cy. Given f(1) = 1 ⇒ c = 1
∴ y = .

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