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Question

A straight line through the point (1,1) meets the X-axis at 'A' and the Y-axis at 'B'. The locus of the mid point of AB is

A
2xy+x+y=0
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B
x+y2xy=0
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C
x+y+2=0
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D
x+y2=0
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Solution

The correct option is C x+y2xy=0
The equation of the straight line in intercept form is
xa+1b=1 ..... (i)
Where a & b are shown in the figure
Since it passes through P (1, 1).
1a+1b=1 or a+b=ab ....... (ii)
Let the coordinates of the mid-point M of AB are (h, k) (a2,b2)
Substitute the values of a and b in (ii), we get 2h+2k=2h×2kh+k=2hk
Hence, the equation of the locus become
x+h=2hkx+y2xy=0

1100033_357873_ans_e0cab0460b154bd983976348dd928c5d.jpg

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