A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² − PB² = 13.

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Q. A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² - PB² = 13.

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For $A(2,4)$ , $B(5,8)$ and general $P(x,y)$ : $PA^2-PB^2=13$ means

\left[(x-2)^2+(y-4)^2\right]-\left[(x-5)^2+(y-8)^2\right]=13.

Expand: $(x^2-4x+4+y^2-8y+16)-(x^2-10x+25+y^2-16y+64)=13$ .

The $x^2,y^2$ cancel: $(-4x-8y+20)-(-10x-16y+89)=13$ . …

Q.A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² − PB² = 13.