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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
6 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
11 months 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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