Question 944672
{{{ (sqrt(x^2+y^2+6x-8y+25))^2=(4+sqrt(x^2+y^2-6x-8y+25))^2  }}}


{{{x^2+6 x+y^2-8y+25 = x^2-6x+y^2-8y+25+8sqrt(x^2-6x+y^2-8y+25)+16}}}


{{{cross(x^2)+6x+cross(y^2)-cross(8y)+25 = cross(x^2)-6x+cross(y^2)-cross(8y)+8sqrt(x^2-6x+y^2-8y+25)+41}}}


{{{6x+25 = -6x+8sqrt(x^2-6x+y^2-8y+25)+41}}}


{{{6x+25 +6x-41=8sqrt(x^2-6x+y^2-8y+25)}}}


{{{12x-16=8sqrt(x^2-6x+y^2-8y+25)}}}  square both sides


{{{(12x-16)^2=8^2(sqrt(x^2-6x+y^2-8y+25))^2}}}


{{{144x^2-384x+256=64(x^2-6x+y^2-8y+25)}}}
  

{{{144x^2-cross(384x)+256=64x^2-cross(384x)+64y^2-512y+1600}}}


{{{144x^2+256-64x^2-64y^2+512y-1600=0}}}


{{{80x^2-64y^2+512y-1344=0}}}  simplify, divide by {{{16}}}


{{{5x^2-4y^2+32y-84=0}}}



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