1.

Let A(5, -4) and B(7, 6) be two points. Find the locus of the point P such that PA : PB = 2 : 3.

Answer»

Let P be (x,y). Then

PA : PB = 2 : 3 

⇒ 3PA = 2 PB

⇒ 9(PA)2 =  4(PB)2 

⇒ 9[(x – 5)2 + (y + 4)2] = 4 [(x - 7)2 + (y - 6)2]

⇒  5x2 + 5y2 - 34x + 120y + 29 = 0

Hence, the equation of the locus is 5x2 + 5y2 34x + 120y + 29 = 0. This equation represent circle



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