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

Options

A. x+y=1
B. x+y=2
C. x+y=2xy
D. 2x+2y=1

Answer

A

Explanation

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.