document.write( "Question 1154857: 1. For the curve x + y^2 -y =1, find equations of all lines tangent to the curve at x=1
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Algebra.Com's Answer #777377 by Edwin McCravy(20055)\"\" \"About 
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document.write( "We want the equations of the two green lines below\r\n" );
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document.write( "The y-coordinates of the two points at x=1 are found by setting x=1 and\r\n" );
document.write( "solving for y:\r\n" );
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document.write( "So the two points of tangency are the points (1,0) and (1,1)\r\n" );
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document.write( "We take the derivative implicitly (i.e., without solving for y),\r\n" );
document.write( "to find the slope m of each of the green tangent lines:\r\n" );
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document.write( "So the slope m of the tangent line at (1,0) is \r\n" );
document.write( "found by setting y equal to the y-coordinate of\r\n" );
document.write( "(1,0), which is 0, in the equation for the \r\n" );
document.write( "derivative above:\r\n" );
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document.write( "So we are looking for the equation of the green line through \r\n" );
document.write( "(1,0) with slope m = 1\r\n" );
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document.write( "That's the equation of the tangent line at (1,0).\r\n" );
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document.write( "Similarly the slope m of the green tangent line at (1,1) is \r\n" );
document.write( "found by setting y equal to the y-coordinate of\r\n" );
document.write( "(1,1), which is 1, in the equation for the \r\n" );
document.write( "derivative above:\r\n" );
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document.write( "So we are looking for the equation of the green line through \r\n" );
document.write( "(1,1) with slope m = -1\r\n" );
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document.write( "That's the equation of the green tangent line at (1,1).\r\n" );
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document.write( "Edwin
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