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I'm not sure where to start with this one. I can do differentiation fairly well, but this question has me stumped. I've come across a few locus questions before, but not sure about the general method and approach when dealing with one of these. Any hints?

Q: A point P(x,y) moves such that its distance from (1,2) is twice its distance from (-3,0). Find the cartesian equation of the locus of P, in its simplest form.

If anyone can help in any way, I appreciate it. Thanks

Zach
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    You don't need calculus for this. Just express the distance rule in terms of x and y, then simplify the resulting equation. – GB supports the mod strike May 27 '18 at 02:53
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    Let $A = (1,2)$, $B = (-3,0)$. 1) write down expressions for $|PA|$ and $|PB|$ in $x,y$. 2) Try to solve $|PA| = 2|PB|$. 3) Too hard to solve because of absolute value. Try to solve $|PA|^2 - 4|PB|^2 = 0$ instead.... – achille hui May 27 '18 at 02:53

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