document.write( "Question 84777: I have a question that states: Find the center and radius of the circle with the given equation: (x-4)^2+(y+8)^2=9. How do I work this? \n" ); document.write( "
Algebra.Com's Answer #61077 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
I have a question that states: Find the center
\n" ); document.write( "and radius of the circle with the given equation:
\n" ); document.write( "(x - 4)² + (y + 8)² = 9. How do I work this?
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document.write( "By memorizing the standard form of a circle, knowing\r\n" );
document.write( "how to compare a given standard form to it, and\r\n" );
document.write( "how to pick out the center and the radius:\r\n" );
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document.write( "Rule:\r\n" );
document.write( "The standard form of a circle is\r\n" );
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document.write( "(x - h)² + (y - k)² = r²\r\n" );
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document.write( "with center (h,k) and radius r.\r\n" );
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document.write( "So compare your equation:\r\n" );
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document.write( "(x - 4)² + (y + 8)² = 9  to\r\n" );
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document.write( "(x - h)² + (y - k)² = r²\r\n" );
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document.write( "and you can see that\r\n" );
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document.write( "-h = -4 or h = 4,\r\n" );
document.write( "-k = +8 or k = -8,\r\n" );
document.write( " r² = 9 so r = 3\r\n" );
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document.write( "So the center is (h,k) = (4,-8) and the radius is r = 3.\r\n" );
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document.write( "You don't need to check it, but let's do it anyway,\r\n" );
document.write( "so you'll know why it's true and learn something\r\n" );
document.write( "about the equation of a circle:\r\n" );
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document.write( "Draw the circle with center (4,-8) and radius = 3\r\n" );
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document.write( "The left-most point of the circle should be 3 units left\r\n" );
document.write( "of the center or (1,-8). \r\n" );
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document.write( "Let's see if that satisfies the\r\n" );
document.write( "equation \r\n" );
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document.write( "(x - 4)² + (y + 8)² = 9\r\n" );
document.write( "(1 - 4)² + (-8 + 8) = 9\r\n" );
document.write( "         (-3)² + 0² = 9\r\n" );
document.write( "              9 + 0 = 9\r\n" );
document.write( "                  9 = 9\r\n" );
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document.write( "Yes it does.\r\n" );
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document.write( "The upper-most point of the circle should be 3 units above\r\n" );
document.write( "the center or (4,-5).  \r\n" );
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document.write( "\r\n" );
document.write( "Let's see if that satisfies the\r\n" );
document.write( "equation \r\n" );
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document.write( "(x - 4)² + (y + 8)² = 9\r\n" );
document.write( "(4 - 4)² + (-5 + 8) = 9\r\n" );
document.write( "       (0)² + (-3)² = 9\r\n" );
document.write( "              0 + 9 = 9\r\n" );
document.write( "                  9 = 9\r\n" );
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document.write( "Yes it does.\r\n" );
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document.write( "The right-most point of the circle should be 3 units right\r\n" );
document.write( "of the center or (7,-8).  \r\n" );
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document.write( "Let's see if that satisfies the\r\n" );
document.write( "equation \r\n" );
document.write( "\r\n" );
document.write( "(x - 4)² + (y + 8)² = 9\r\n" );
document.write( "(7 - 4)² + (-8 + 8) = 9\r\n" );
document.write( "          (3)² + 0² = 9\r\n" );
document.write( "              9 + 0 = 9\r\n" );
document.write( "                  9 = 9\r\n" );
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document.write( "Yes it does.\r\n" );
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document.write( "The lowest point of the circle should be 3 units below\r\n" );
document.write( "of the center or (4,-11).  \r\n" );
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document.write( "\r\n" );
document.write( "Let's see if that satisfies the\r\n" );
document.write( "equation \r\n" );
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document.write( " (x - 4)² + (y + 8)² = 9\r\n" );
document.write( "(4 - 4)² + (-11 + 8) = 9\r\n" );
document.write( "        (0)² + (-3)² = 9\r\n" );
document.write( "              0 + 9 = 9\r\n" );
document.write( "                  9 = 9\r\n" );
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document.write( "Yes it does.  So we know the center is (4,-8) and the radius \r\n" );
document.write( "is 3.\r\n" );
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document.write( "Edwin
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