A tangent to the curve,\small y=f (x) at P(x, y)

meets x-axis at A and y-axis at B.  If AP : BP=1 : 3 and \small f(1)=1, then the curve also passes through the point :

 

  • Option 1)

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

  • Option 2)

    \left ( \frac{1}{2},4 \right )

  • Option 3)

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

  • Option 4)

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

 

Answers (1)
V Vakul

 

Selection formula -

x= \frac{mx_{2}+nx_{1}}{m+n}

y= \frac{my_{2}+ny_{1}}{m+n}

- wherein

If P(x,y) divides the line joining A(x1,y1) and B(x2,y2) in ration m:n

 

 

Slope of a line -

m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

- wherein

Slope of line joining A(x1,y1) and  B(x2,y2) .

 

 We have,

x=\frac{3a}{4},y=\frac{b}{4}\Rightarrow a=\frac{4x}{3},b=4y

Now, Slope=m=\frac{-b}{a}= \frac{-3y}{x}

Also, slope = \frac{dy}{dx}\Rightarrow \frac{dy}{dx}= \frac{-3y}{x}

\Rightarrow \ln y=-3\ln x+c

\Rightarrow c=0

So,

y=\frac{1}{x^3}

 

 


Option 1)

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

Option 2)

\left ( \frac{1}{2},4 \right )

Option 3)

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

Option 4)

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

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