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Given A=(1,1) and A B is any line throug...

Given `A=(1,1)` and `A B` is any line through it cutting the x-axis at `Bdot` If `A C` is perpendicular to `A B` and meets the y-axis in `C` , then the equation of the locus of midpoint `P` of `B C` is (a) `x+y=1` (b) `x+y=2` (c) `x+y=2x y` (d) `2x+2y=1`

A

x+y=1

B

x+y=2

C

x+y=2xy

D

2x+2y=1

Text Solution

Verified by Experts

The correct Answer is:
A
The equation of line AB is y-1 = m(x-1). Therefore, the equation of line AC is
`y-1 = -(1)/(m)(x-1)`

`2h=1-(1)/(m)`
`2k=1+(1)/(m)`
Eliminating m, we have locus x+y=1.
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