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A curve is traced by a point $P(x,y)$ which moves such that its distance from the point $A(-1,1)$ is three times its distance from the point $B(2,-1)$. Determine the equation of the curve.

I have only one question. And that is the only thing I need answered at this time. My question to you is, when it says "which moves such that its distance from the point..." by distance, does it mean the slope from $P(x,y)$ to $A(-1,1)$ is three times the distance than from$P(x,y)$ to $B(2,-1)$? Please answer only this and nothing else. I will re-edit with further findings.

Edit: To find the next points would it be logical to use this equation:

$d=distance$ and $P=(x,y)$ $d(P,(-1,1))=3d(P,(2,-1))$ $d\sqrt{(-1\pm x_1)^2+(1\pm y_1)^2}=3d\sqrt{(2\pm x_1)^2+(-1\pm y_1)^2}$ And from here I would use $P=(x,y)$ and plug in any values of $x$ and $y$ to try and find my equation. Would this be correct?

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    Okay, so I got: $8\left((x^2-\frac{19}{4}x)(y^2+\frac{5}{2}y)+\frac{43}{8}\right)$ and then complete the square?2012-08-07

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At all points on the curve the distance from $P$ to $A$ should be three times the distance from $P$ to $B$.

I recommend first sketching this by hand. Then use the distance formula to find the equation of the curve. Finally, make sure both answers agree!

Let $d(P,Q)$ represent the distance between points $P$ and $Q$. The problem statement tells us that $d(P,A) = 3 d(P,B).$ Plug in $(x,y)$ for $P$ and the given values of $A$ and $B$ to find the equation for the curve.

Hint: After some algebra you will find it is one of the conic sections.

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    @AustinBroussard: Yes, that is exactly right. Use $(x,y)$ for $P$ and you will find an equation in $y$ and $x$. Square both sides and simplify and you will find the equation of a circle. I will be signing off now. Good night and good luck!2012-07-24
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The distance between two points is not the slope. For example, the distance between $(1,2)$ and $(6,9)$ is $\sqrt{74}$. No more, since you asked for minimal help. And congratulations for that!

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    @AustinBroussard: Yes, that is good.2012-07-24