What is the equation of this curve?
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Answer:
distance formula d=sqrt((x-x1)^2+(y-y1)^2) so using your points the distance from A (call it dA) and from B (call it dB) dA=3*dB giving sqrt [(x+1)^2+(y-1)^2]=3*sqrt[(x-2)^2+(y+1)^2... depending on how simplified you want the answer you can multiply it out and square both sides to get rid of the radicals After I multiplied it out and combined all like terms I have 8x^2-38x+35+8y^2+20y+8=0
grannie at Yahoo! Answers Visit the source
Other answers
distance formula d=sqrt((x-x1)^2+(y-y1)^2) so using your points the distance from A (call it dA) and from B (call it dB) dA=3*dB giving sqrt [(x+1)^2+(y-1)^2]=3*sqrt[(x-2)^2+(y+1)^2… depending on how simplified you want the answer you can multiply it out and square both sides to get rid of the radicals After I multiplied it out and combined all like terms I have 8x^2-38x+35+8y^2+20y+8=0
grannie
[(y-1)^2 +(x+1)^2]^1/2 = 3[(y+1)^2 +(x-2)^2]^1/2 (y^2+1-2y +x^2+1+2x) = 9(y^2+1+2y +x^2-4x+4) y^2-2y+x^2+2x+2=9y^2+18y+9x^2-36x+45 , ====> 8y^2+8x^2+20y-38x+43=0 This is as far as I could go.
nozar nazari
If D1 = distance of P from A: D1^2 = (x+1)^2 + (y-1)^2 D2 = dist from B: D2^2 = (x-2)^2 + (y+1)^2 D1 = 3.D2 D1^2 = 9. D2^2 (x+1)^2 + (y-1)^2 = 9 [(x-2)^2 + (y+1)^2] (x+1)^2 + (y-1)^2 = 9 (x-2)^2 + 9(y+1)^2 Expand and simplify.
efqy
If D1 = distance of P from A: D1^2 = (x+1)^2 + (y-1)^2 D2 = dist from B: D2^2 = (x-2)^2 + (y+1)^2 D1 = 3.D2 D1^2 = 9. D2^2 (x+1)^2 + (y-1)^2 = 9 [(x-2)^2 + (y+1)^2] (x+1)^2 + (y-1)^2 = 9 (x-2)^2 + 9(y+1)^2 Expand and simplify.
efqy
[(y-1)^2 +(x+1)^2]^1/2 = 3[(y+1)^2 +(x-2)^2]^1/2 (y^2+1-2y +x^2+1+2x) = 9(y^2+1+2y +x^2-4x+4) y^2-2y+x^2+2x+2=9y^2+18y+9x^2-36x+45 , ====> 8y^2+8x^2+20y-38x+43=0 This is as far as I could go.
nozar nazari
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