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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 P of 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=mx−1. Therefore , the equation of line AC is y−1=1mx−12h=1−1m2k=1+1mEliminating m, we have locus x+y=1
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