If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA² = 3PB².

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Q. If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA² = 3PB².

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Let $P(x,y)$ satisfy $PA^2=3PB^2$ for $A(4,1)$ , $B(5,4)$ :

(x-4)^2+(y-1)^2=3\left[(x-5)^2+(y-4)^2\right].

Left side: $x^2-8x+16+y^2-2y+1$ . Right side: $3(x^2-10x+25)+3(y^2-8y+16)=3x^2-30x+75+3y^2-24y+48$ .

So $x^2-8x+16+y^2-2y+1=3x^2-30x+75+3y^2-24y+48$ . …

Q.If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA² = 3PB².