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Question

# If the area of the triangle formed by the lines y=x, x+y=2 and the line through P(h,k) and parallel to x-axis is 4h2, the locus of P can be

A

2xy+1=0

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B

2x+y1=0

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C

x2y+1=0

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D

x+2y1=0

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Solution

## The correct options are A 2x−y+1=0 B 2x+y−1=0 Coordinates of A are (1,1) which is the point of intersection of the given lines. y=k is the line through P parallel to x-axis which meets the given lines at B and C. So coordinates of B are (k,k) and C are (2−k,k). Area of ΔABC=12∣∣ ∣∣111kk12−kk1∣∣ ∣∣=4h2 ⇒ (k−1)2=4h2⇒k−1=±2h Locus of P(h,k) is y−1=±2x ⇒ 2x−y+1=0 or 2x+y−1=0

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