Question

# The area of the triangle formed by the intersection of a line parallel to xâˆ’axis and passing through P(h,k) with the lines y=x and x+y=2 is 4h2. Then the locus of the point P is

A
y=3x2 or y=3x2
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B
y=2x1 or y=2x1
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C
y=3x+2 or y=3x+2
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D
y=2x+1 or y=2x+1
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Solution

## The correct option is D y=2x+1 or y=−2x+1A line passing through P(h,k) and parallel to x− axis is y=k ........................(1)The other two given lines are y=x ........................(2)and x+y=2 .........................(3)Solving eqns (1) and (2)we get A(k,k)Solving eqns (2) and (3)we get B(1,1)Solving eqns (3) and (1)we get C(2−k,k)∴ Area of △ABC=4h2⇒12∣∣ ∣∣kk11112−kk1∣∣ ∣∣=4h2Applying C2→C2−C1, then12∣∣ ∣∣k011012−k2k−21∣∣ ∣∣=4h2⇒(k−1)2=4h2⇒k−1=±2h∴k=±2h+1Replace h→x,k→y ∴ Locus of (h,k) is y=2x+1 or y=−2x+1

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