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Question

If the coordinates of two points A and B are (3,4) and (5,-2) respectively. Then, the coordinates of any point P, if PA = PB and area of Δ PAB = 10, are


A

(7, 5), (1, 0)

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B

(7, 2), (1, 0)

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C

(7, 2), (- 1, 0)

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D

(2, 7), (1, 0)

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Solution

The correct option is B

(7, 2), (1, 0)


Let the coordinates of P be(x,y). Then,PA=PBPA2=PB2(x3)2+(y4)2=(x5)2+(y+2)2x3y1=0 (i)Now,Area of ΔPAB=1012∣ ∣xy1341521∣ ∣=±106x+2y26=±206x+2y46=0 or 6x+2y6=03x+y23=0 or 3x+y23=0Solving x3y1=0 and 3x+y23=0We get x=7,y=2Solving x3y1=0 and 3x+y=30We get x=1,y=0Thus,the cordinates of P are (7,2) or (1,0).Hence,(b) is the correct answer.


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