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# The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P (h, k) with the lines y = x and x + y = 2 is 4h^2. Find the locus of the point P.

Arun Kumar IIT Delhi
7 years ago
Hello Student,

Area of triangle=(1/2).AB.AC=4h^2
and AB= 2|k–1|=AC
=>4h2 =(1/2).2.(k–1)^2
=>k-1 = ± 2h.
=>locus is y = 2x + 1, y = – 2x + 1.
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Ritesh
13 Points
one year ago
Hello friends
This solution is for those who might be getting problem while calculating area
With the given points apply the area formula as
2-k        k.        1
1.          1.        1.    =8h^2
k.          k.         1
Solving further
(2-k)(1-k)-k(1-k)=8h^2
(1-k)(2-2k)=8h^2
(1-k)^2=4h^2
1-k=+2h  or  - 2h