Loser66
  • Loser66
\(\sqrt{(x+3)^2+(y-2)^2}=\sqrt{(x-3)^2+y^2}\) In the xy plane, the set of points whose coordinates satisfy the equation above is?? 1) A line 2) A circle 3) An ellipse 4) A parabola 5) One branch of a hyperbola Please, help
Mathematics
katieb
  • katieb
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ganeshie8
  • ganeshie8
Notice the distance formulas on left and right hand sides, the given equation is same as : ``` distance between (x,y) and (-3, 2) = distance between (x, y) and (3, 0) ```
ganeshie8
  • ganeshie8
so you need to find the locus of points that stay at same distance from two points : (-3, 2) and (3, 0)
ganeshie8
  • ganeshie8
Thats exactly the definition of perpendicular bisector!

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Loser66
  • Loser66
Got you, thank you so much.
Loser66
  • Loser66
Damn!! They are distance formulas!! how can I not see it!!
ganeshie8
  • ganeshie8
Haha solving them is fun too, square both sides and all quadratic terms cancel out.. gives the equation of perpendicular bisector..
Loser66
  • Loser66
I did that way but stop at square both sides and look at the square of x and y, I think there must be other way to find the answer out quickly. So that I stopped and post the question. hehehe... I got it from you. Thank you so much
ganeshie8
  • ganeshie8
np

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