    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.

A

y=2x+1

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B

y=-2x+1

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C

y-2x+1 = 0

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D

2y-x+1 = 0

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Solution

## The correct options are A y=2x+1 B y=-2x+1 Finding B–––––––––––– It is the intersection of y=x and y=k ⇒ (k,k) is the point of intersection. Finding A–––––––––––– It is the intersection of y=x and x+y=2 ⇒ (1,1) is A. Finding C–––––––––––– C is the intersection of y=x and x+y=2 ⇒ (2-k,k) is C. Area of △=12 AD×BC BC=2-k-k = 2-2k AD=k-1 Area of △=12 2(1−k)(k−1) =(k−1)2(Area is +ve) This is given as 4h2 ⇒ 4h2=(k−1)2 2h=±(k−1) ⇒ 2h−k+1=0 or 2h+k−1=0 Replace(h,k) with (x,y) ⇒ 2x-y+1=0 or 2x+y-1=0 Or y=2x+1 or y=-2x+1  Suggest Corrections  9      Similar questions  Related Videos   Basic Concepts
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