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Question

Find the locus of the point P for which of the distance from P to (4, 0) is double the distance from P to x-axis .

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Solution

Let P be (x,y)
Distance from (4,0)
(x4)2+y2x24x+16+y2x2+y24x+16(1)
Distance from Origin
x2+y2
According to Question

x2+y24x+16=2x2+y2
Squaring on both sides
(x2+y24x+16)=4(x2+y2)3x2+3y2+4x16=0


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