A variable line drawn through the point (1,3) meets the x-axis at A and y-axis at B. If the rectangle OAPB is completed, where 'O' is the origin, the locus of 'P' is

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1y+3x=1

x+3y=1

1x+3y=1

3x+y=1

answer is C.

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Detailed Solution

Let the line be xa+yb=1, then 1a+3b=1 A≡(a,0),B(0,b) ⇒ P≡(a,b) Thus locus of 'p' is 1x+3y=1 .

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