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