Determining the equation of a curve

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SUMMARY

The discussion focuses on determining the equation of a curve traced by a point P (x,y) based on its distances from two fixed points A (-1,1) and B (2,-1). The key conclusion is that the distance from point A to point P must equal three times the distance from point B to point P. Participants suggest using the distance formula to establish the relationship between these distances and derive the equation of the curve.

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  • Familiarity with algebraic manipulation of equations
  • Basic knowledge of conic sections and their properties
  • Ability to translate geometric relationships into mathematical equations
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Homework Statement



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.

Homework Equations





The Attempt at a Solution



used distance formulas to find A is the squareroot of 13 away from B.

how do i find the curve
 
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I would try to translate what the problem says in words into equations.

You're told that the distance from point A to point P is always 3 times the distance from point B to point P.

So it seems to me that the way to proceed is to write down an expression for the distance from A to P and set it equal to the expression for the distance from B to P multiplied by 3.
 
You should try applying the distance formula for the problem as you described it. That should help you to start.
 

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