document.write( "Question 1137032: find the equation describing all points equidistant from the x-axis and the point (0,2)
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Algebra.Com's Answer #754872 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by @MathLover1 is incorrect.\r
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\n" ); document.write( "\n" ); document.write( "            It is incorrect, because the formula for the distance from the point (0,2) to the point (x,y) is    $\"sqrt%28x%5E2+%2B+%28y-2%29%5E2%29\"$ , and not    $\"sqrt%28x%5E2+-+%28y-2%29%5E2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "            The final curve should be a parabola, not a hyperbola.\r
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\n" ); document.write( "\n" ); document.write( "            I know it very well, since I solved similar problems several times at this forum.\r
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\n" ); document.write( "\n" ); document.write( "            The correct solution is below.\r
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document.write( "The distance from  (, ) to the x-axis is  |y|.\r\n" );
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document.write( "The distance from   (, ) to the point (, ) is  .\r\n" );
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document.write( "The base equation is\r\n" );
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document.write( "|y| = .\r\n" );
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document.write( "Square both sides of this equation and solve for.  \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( "4y =  \r\n" );
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document.write( "y =     <==========>  parabola with the branches upward; the vertex at the point (0,1)\r\n" );
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document.write( "    \r\n" );
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document.write( "                Plot  y =  + 1\r\n" );
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