document.write( "Question 1111770: A circle is tangent to both the x and y-axis and the equation x+y=8. what are the equations of the circle? \n" ); document.write( "

Algebra.Com's Answer #726793 by ikleyn(52812) $\"\"$ $\"About$

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\n" ); document.write( "A circle is tangent to both the x and y-axis and the equation x+y=8. what are the equations of the circle?
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\n" ); document.write( "\n" ); document.write( "The formulation is, OBVIOUSLY, not exactly correct and, therefore, is not pure Math.\r
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\n" ); document.write( "\n" ); document.write( "The correct formulation, simultaneously from the Math and the Grammar point of view, is THIS:\r
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document.write( "    A circle is tangent to both the x and y-axis and to the straight line with the equation x+y=8.  Find the circles.\r\n" );
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document.write( "Since the circle is tangent to both the x and y-axis, its center lies at the bisector of the first quadrant angle  x = y,  and  r = x = y.\r\n" );
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document.write( "Now we have two cases   (see the Figure below).\r\n" );
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document.write( "Case 1.  Small circle inside the triangle.\r\n" );
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document.write( "Coordinates of the center via the radius  x = y = r.\r\n" );
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document.write( "Coordinates of the tangent point via the radius   =  = .\r\n" );
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document.write( "Since   +  = 8,  it gives an equation for \"r\"\r\n" );
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document.write( "     +  +  +  = 8,\r\n" );
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document.write( "     = 4  ====>  r =  = 2.34 (approx.)\r\n" );
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document.write( "Plot   x + y = 8   and two circles. \r\n" );
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document.write( "Case 2.  Large circle outside the triangle.\r\n" );
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document.write( "Coordinates of the center via the radius  x = y = R.\r\n" );
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document.write( "Coordinates of the tangent point via the radius   =  = .\r\n" );
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document.write( "Since   +  = 8,  it gives an equation for \"R\"\r\n" );
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document.write( "     -  +  -  = 8,\r\n" );
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document.write( "     = 4  ====>  R =  = 13.66 (approx.)\r\n" );
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document.write( "Answer.  Small circle radius  r =  = 2.34 (approx.) and the center  x = y = r.  The equation is   +  = .\r\n" );
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document.write( "         Large circle radius  R =  = 13.66 (approx.) and the center  x = y = R.   The equation is    +  = .\r\n" );
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