document.write( "Question 398173: Hai Sir, please help me on this problem, i got stuck \r
\n" ); document.write( "\n" ); document.write( "2)The centre of a circle is (2x-1,7) and it passes through the point (-3,-1).If the diameter of the circle is 20units ,then find the values of x.\r
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Algebra.Com's Answer #282152 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Hai Sir, please help me on this problem, i got stuck
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\n" ); document.write( "2)The centre of a circle is (2x-1,7) and it passes through the point (-3,-1).If the diameter of the circle is 20units ,then find the values of x.
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document.write( "The letter x is normally a variable, not an unknown constant.  However the x\r\n" );
document.write( "in (2x-1,7) represents an unknown constant.  So to avoid conflict of notation\r\n" );
document.write( "involving x as a variable and x as an unknown constant, I will change the x\r\n" );
document.write( "in the point to \"a\", which is a standard letter to use for an unknown constant.\r\n" );
document.write( "So let's pretend the problem was stated this way instead:\r\n" );
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\n" ); document.write( "2)The centre of a circle is (2a-1,7) and it passes through the point (-3,-1).
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document.write( "The equation of a circle with center (h,k) and radius r is\r\n" );
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document.write( "(x - h)² + (y - k)² = r²\r\n" );
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document.write( "So we substitute (h,k) = (2a-1,7), and since the diameter\r\n" );
document.write( "of the circle is 20 units, the radius is one-half that or r=10 \r\n" );
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document.write( "(x - (2a-1))² + (y - 7)² = 10²\r\n" );
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document.write( "Since we know that (-3,-1) is a point on the circle, we can substitute\r\n" );
document.write( "(x,y) = (-3,-1)\r\n" );
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document.write( "(-3 - (2a-1) )² + (-1 - 7)² = 10²\r\n" );
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document.write( "     (-3 - 2a + 1)² + (-8)² = 100\r\n" );
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document.write( "              (-2-2a)² + 64 = 100\r\n" );
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document.write( "                   (-2-2a)² = 36\r\n" );
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document.write( "                    -2 - 2a = ±√36\r\n" );
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document.write( "                    -2 - 2a = ±6\r\n" );
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document.write( "Using the +          Using the -\r\n" );
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document.write( "-2 - 2a =  6         -2 - 2a = -6                        \r\n" );
document.write( "    -2a =  8             -2a = -4\r\n" );
document.write( "      a = -4               a = 2\r\n" );
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document.write( "(x - (2a-1))² + (y - 7)² = 10²\r\n" );
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document.write( "Using the + that becomes                 \r\n" );
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document.write( "(x - (2(-4)-1))² + (y - 7)² = 10²   \r\n" );
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document.write( "(x - (-8-1))² + (y - 7)² = 10²\r\n" );
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document.write( "(x - (-9))² + (y - 7)² = 10²\r\n" );
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document.write( "(x + 9)² + (y - 7)² = 10²\r\n" );
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document.write( "That's this red circle:\r\n" );
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document.write( "(x - (2a-1))² + (y - 7)² = 10²\r\n" );
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document.write( "Using the - that becomes                 \r\n" );
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document.write( "(x - (2(2)-1))² + (y - 7)² = 10²   \r\n" );
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document.write( "(x - (4-1))² + (y - 7)² = 10²\r\n" );
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document.write( "(x - (3))² + (y - 7)² = 10²\r\n" );
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document.write( "(x - 3)² + (y - 7)² = 10²\r\n" );
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document.write( "That's the green circle:\r\n" );
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document.write( "Notice they both go through the point (-3,-1); in fact they intersect\r\n" );
document.write( "at that point and both have radius 10 and diameter 20. \r\n" );
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document.write( "So the answers are a = -4 and a = 2.  \r\n" );
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document.write( "Edwin
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