document.write( "Question 1089223: The graph of 2y^4 -x^2 +11 =0 is symmetric with respect which of the following?
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Algebra.Com's Answer #703563 by ikleyn(52858)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The graph of 2y^4 -x^2 +11 =0 is symmetric with respect which of the following?\r\n" );
document.write( " 1. The x axis \r\n" );
document.write( " 2. The y axis \r\n" );
document.write( " 3. The origin \r\n" );
document.write( "A) only 1\r\n" );
document.write( "B) only 2\r\n" );
document.write( "C) only 3\r\n" );
document.write( "D) 1, 2, and 3\r\n" );
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document.write( "Plot y1 = \"root%284%2C%28x%5E2-11%29%2F2%29%29\" (red)  and y2 = \"-root%284%2C%28x%5E2-11%29%2F2%29%29\" (green).\r\n" );
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\n" ); document.write( "\n" ); document.write( "      The correct answer is  OPTION  D).\r
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document.write( "0.  Let the point (x,y) belongs to the curve.\r\n" );
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document.write( "    It means that its coordinates satisfy the equation \r\n" );
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document.write( "    2y^4 -x^2 +11 =0.     (1)\r\n" );
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document.write( "1.  Then the point (-x,y) also belongs to the curve.\r\n" );
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document.write( "    Indeed, then 2y^4 - (-x)^2 + 11 = 2y^4 - x^2 + 11 = 0 due to (1).\r\n" );
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document.write( "    It means that the symmetry  (x,y) --> (-x,y)  relative to the axis \"Y\" is in place.\r\n" );
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document.write( "2.  Also, then the point (x,-y) belongs to the curve.\r\n" );
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document.write( "    Indeed, then 2(-y)^4 - x^2 + 11 = 2y^4 - x^2 + 11 = 0 due to (1).\r\n" );
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document.write( "    It means that the symmetry  (x,y) --> (x,-y)  relative to the axis \"X\" is in place.\r\n" );
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document.write( "3.  Finally, then the point (-x,-y) belongs to the curve.\r\n" );
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document.write( "    Indeed, then 2(-y)^4 - (-x)^2 + 11 = 2y^4 - x^2 + 11 = 0 due to (1).\r\n" );
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document.write( "    It means that the symmetry  (x,y) --> (-x,-y)  relative to the origin is in place.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus my statement is  PROVED  and the solution is  COMPLETED.\r
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\n" ); document.write( "\n" ); document.write( "        Proved.   Solved.   And completed. \r
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\n" ); document.write( "\n" ); document.write( "The other's tutor solution is   WRONG   (his approach is   WRONG   and his answer is   UNCOMPLETED).\r
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