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Explanation

Here, the triangle formed by a line parallel to `X`-axis passing through `P(h,k)` and the straight line `y=x` and `y=2-x` could be as shown below :

Since, area of `DeltaABC=4h^(2)`
`:. (1)/(2)AB*AC=4h^(2)`
where, `AB=sqrt(2)|k-1|` and `AC=sqrt(2)(|k-1|)`
`implies(1)/(2)*2(k-1)^(2)=4h^(2)`
`implies4h^(2)=(k-1)^(2)`
`implies2h=+-(k-1)`
The locus of a point is `2x=+-(y-1)`.