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Question

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 4h2. Find the locus of the point P.

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Solution

ar(ABC)=12∣ ∣2kk1kk1111∣ ∣=4h2
∣ ∣2kk1kk1111∣ ∣=8h2
(2k)[k11]k(k1)+1(kk)=4h2
(2h)(k2)k2+k=4h2
2kk24+2kk2+k=4h2
5k2k244h2
2k25k+4h2+4=0
2y25y+4x2+4=0
Locus P is 4x2+2y25y+4=0
Hence, solved.

1169169_878801_ans_9774e438810e4724912e97c077ce3a29.png

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