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Question

A tangent drawn to the curve y=f(x) at P(x,y)
cuts the x and y axes at A and B, respectively, such that AP:PB=1:3. If f(1)=1 then the curve passes through (k,18) where k is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is A 1
Equation of tangent at P(x,y) is

Yy=dydt(Xx)

It meets x - axis at A

A=(xdxdyy,0)

and y -axis at B

B=(0,ydydt)

And also given APPB=1:3

Using section formula

[mx1+m2x2m1m+m2,m1y1+m2y2m1+m2]

34(xdxdyy)v=14(yxdydx)=(x,y)

34(xydxdy)=x; 14(yxdyx)=y

3dxx+dyy=0

log(x3y)= const (on integrative)

Given f(1)=1, so here const=1

x3y=1 (k, 1/8)

k3=8

k=2

1331071_1107146_ans_c4d4706b3f1e499a93282a153729ec90.png

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