question_answer

A tangent to the curve, \[y=f(x)\] at \[P(x,\,y)\] meets x-axis at A and y-axis at B. If \[AP:BP=1:3\] and \[f(1)=1,\] then the curve also passes through the point: [JEE Online 09-04-2017]

A)  \[\left( \frac{1}{3},\,24 \right)\]                               

B)  \[\left( \frac{1}{2},4 \right)\]

C)  \[\left( 2,\frac{1}{8} \right)\]                    

D)  \[\left( 3,\,\frac{1}{28} \right)\]