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Question

Find the equation of the locus of P, if A=(4,0),B=(4,0) and |PAPB|=4.

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Solution

Given,
A=(4,0)(x1,y1),B=(4,0)(x2,y2)

|PAPB|=4

Distance Formula =(xx1)2+(yy1)2

(x4)2+(y0)2(x+4)2+(y0)2=4

(x4)2+y2=16+(x+4)2+y

4x2+4+8x=x2+16+8x+y2

3x2y2=12

x24y212=1

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