Q.

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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a

1y+3x=1

b

x+3y=1

c

1x+3y=1

d

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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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