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Q.

Given A≡(1,1) and AB is any line through it cutting the x -axis at B . If AC is perpendicular to AB and meets the y -axis in C , then the equation of the locus of midpoint Pof BC is

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a

x+y=1

b

x+y=2

c

x+y=2xy

d

2x+2y=1

answer is A.

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Detailed Solution

The equation of line AB is y−1=m(x−1) . Therefore, the  equation of line AC is y−1=−1m(x−1)2h=1−1m2k=1+1m Eliminating m , we have locus x+y=1 .
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