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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.

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.
 

Grade:10

2 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
10 years ago
Hello Student,
221-1323_Screen Shot 2014-07-08 at 1.09.12 pm.png
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
Askiitians Faculty
Ritesh
13 Points
4 years 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

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