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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

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hello Student,
221-2376_Screen Shot 2014-07-08 at 1.27.02 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

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