Let a point P be such that its distance from the point (5,0) is thrice the distance of P from the point (−5,0). If the locus of the point P is a circle of radius r, then 4r2 is equal to
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Solution
Let P be (h,k),A(5,0) and B(−5,0)
Given PA=3PB ⇒PA2=9PB2 ⇒(h−5)2+k2=9[(h+5)2+k2] ⇒8h2+8k2+100h+200=0 ∴ Locus of P is x2+y2+(252)x+25=0
Centre ≡(−254,0) ∴r2=(−254)2−25 =62516−25=22516 ∴4r2=4×22516=2254=56.25