document.write( "Question 233394: sketch the portion of graph in the first quadrant and use symmetry to complete the rest of the graph\r
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Algebra.Com's Answer #172294 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It's symmetrical with respect to the x-axis \r\n" );
document.write( "because if we replace x by -x and simplify, we\r\n" );
document.write( "get the same equation we started with:\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "\"4%28-x%29%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "It's symmetrical with respect to the y-axis also \r\n" );
document.write( "because if we replace y by -y and simplify, we\r\n" );
document.write( "get the same equation we started with:\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "\"4x%5E2%2B16%28-y%29%5E2=16\"\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "It's symmetrical with respect to the origin \r\n" );
document.write( "because if we replace x by -x and y by -y\r\n" );
document.write( "at the same time and simplify, we also\r\n" );
document.write( "get the same equation we started with:\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "\"4%28-x%29%5E2%2B16%28-y%29%5E2=16\"\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "Next we find some first quadrant points.\r\n" );
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document.write( "Choose \"x=0\"\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "\"4%280%29%5E2%2B16y%5E2=16\"\r\n" );
document.write( "\"0%2B16y%5E2=16\"\r\n" );
document.write( "\"16y%5E2=16\"\r\n" );
document.write( "\"y%5E2=1\"\r\n" );
document.write( "\"y%5E2-1=0\"\r\n" );
document.write( "\"%28y-1%29%28y%2B1%29=0\"\r\n" );
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document.write( "This gives \"y=1\" and \"y=-1\"\r\n" );
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document.write( "So a point in the first quadrant is (0,1)\r\n" );
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document.write( "(Actually it's a point on the BORDER of the first\r\n" );
document.write( "quadrant, on the y-axis)\r\n" );
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document.write( "Choose \"x=1\"\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "\"4%281%29%5E2%2B16y%5E2=16\"\r\n" );
document.write( "\"4%2B16y%5E2=16\"\r\n" );
document.write( "\"16y%5E2=12\"\r\n" );
document.write( "\"y%5E2=12%2F16\"\r\n" );
document.write( "\"y%5E2=3%2F4\"\r\n" );
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document.write( "This gives \"y=sqrt%283%29%2F2\" and \"y=-sqrt%283%29%2F2\"\r\n" );
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document.write( "So a point in the first quadrant is (0,\"sqrt%283%29%2F2\"),\r\n" );
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document.write( "which is about (1, .9)\r\n" );
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document.write( "Choose \"x=2\"\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "\"4x%5E2%2B16y%5E2=16\"\r\n" );
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document.write( "\"4%282%29%5E2%2B16y%5E2=16\"\r\n" );
document.write( "\"4%284%29%2B16y%5E2=16\"\r\n" );
document.write( "\"16%2B16y%5E2=16\"\r\n" );
document.write( "\"16y%5E2=0\"\r\n" );
document.write( "\"y%5E2=0\"\r\n" );
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document.write( "This gives \"y=0\" \r\n" );
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document.write( "So another point in the first quadrant is (2,0)\r\n" );
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document.write( "(Actually it's another point on the BORDER of the first\r\n" );
document.write( "quadrant, this time on the x-axis)\r\n" );
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document.write( "Plot those three first quadrant points:\r\n" );
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document.write( "Next by the symmetry, we can reflect these three points\r\n" );
document.write( "in both the x-axis and the y-axis, (like a mirror!) and \r\n" );
document.write( "we have this:\r\n" );
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document.write( "Now we can sketch the curve:\r\n" );
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document.write( "Edwin
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