document.write( "Question 62660: find the equation of the set of all points such that the differences of the distances of P(x,y) from (0,-3) and (0,3) is 1. \n" ); document.write( "

Algebra.Com's Answer #43456 by jai_kos(139) $\"\"$ $\"About$

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Given a point P(x, y), ( 0 , -3) and ( 0 ,3)\r
\n" ); document.write( "\n" ); document.write( "The difference of the distance between the point from P(x ,y) to ( 0 ,-3) and \r
\n" ); document.write( "\n" ); document.write( "the distance of the point from p(x ,y) to ( 0 ,3) is 1.\r
\n" ); document.write( "\n" ); document.write( "sqrt [(0 -x)^2 + (-3 - y)^2] - sqrt [(0-x) ^2 + ( 3-y)^2] = 1\r
\n" ); document.write( "\n" ); document.write( "==>Sqrt[ x^2 + 9 + y^2 + 6y ] = 1 + sqrt [ x^2 + 9 + y^2 -6y] \r
\n" ); document.write( "\n" ); document.write( "Squaring on both sides we get\r
\n" ); document.write( "\n" ); document.write( "{ Sqrt[ x^2 + 9 + y^2 + 6y ]}^2 = {1 + sqrt [ x^2 + 9 + y^2 -6y]} ^2\r
\n" ); document.write( "\n" ); document.write( "x^2 + 9 + y^2 + 6y = 1 + x^2 + 9 + y^2 -6y + 2 * 1 * sqrt [ x^2 + 9 + y^2 -6y]\r
\n" ); document.write( "\n" ); document.write( "6y + 6y - 1 = 2 sqrt(x^2 + 9 + y^2 -6y)\r
\n" ); document.write( "\n" ); document.write( "12y - 1 = 2 sqrt(x^2 + 9 + y^2 -6y)\r
\n" ); document.write( "\n" ); document.write( "Square on both sides, we get\r
\n" ); document.write( "\n" ); document.write( "(12y - 1)^2 = 4 (x^2 + 9 + y^2 -6y)\r
\n" ); document.write( "\n" ); document.write( "12y^2 + 1 -24y = 4x^2 + 36 + 4y^2 -24y \r
\n" ); document.write( "\n" ); document.write( "Bring all the terms to right hand side, we get\r
\n" ); document.write( "\n" ); document.write( "4x^2 -12y^2 + 4y^2 + 36 -1 = 0\r
\n" ); document.write( "\n" ); document.write( "4x^2 -8y^2 + 35 = 0 \n" ); document.write( "

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