document.write( "Question 273320: A circle with a radius of 4 and a midpoint at (2,2) \n" ); document.write( "
Algebra.Com's Answer #199754 by Edwin McCravy(20054) $\"\"$ $\"About$
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A circle with a radius of 4 and a midpoint at (2,2)
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document.write( "It is unusual to call the center (or \"centre\" if you are from the UK)\r\n" );
document.write( "of a circle by the term \"midpoint\".  We usually use the word \"midpoint\"\r\n" );
document.write( "for the midpoint of a line segment, or for the midpoint between two \r\n" );
document.write( "given points.  But I will take it that by \"midpoint\", you mean \"center\"\r\n" );
document.write( "or \"centre\".\r\n" );
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document.write( "So I assume you want the equation of this green circle, with the center \r\n" );
document.write( "at (2,2), the point so marked below:\r\n" );
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document.write( "Then you must learn the standard form for the equation of a\r\n" );
document.write( "circle which has center at (h,k) and radius r:\r\n" );
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document.write( "If you know that formula by heart, then all you have to do is\r\n" );
document.write( "substitute h=2, k=2 since (h,k) = (2,2) and r=4, and instantly\r\n" );
document.write( "you have\r\n" );
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document.write( "That's it except for the tiny task of squaring the 4\r\n" );
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document.write( "except that it is better not to acrtually square the\r\n" );
document.write( "radius.  Why? The standard form was created because\r\n" );
document.write( "they wanted to get equations in forms so that you can\r\n" );
document.write( "tell how the graph is going to look just by looking at \r\n" );
document.write( "the equation.\r\n" );
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document.write( "You don't need to multiply that out at all. Just leave it\r\n" );
document.write( "in standard form.  The beauty of the standard form is that\r\n" );
document.write( "you can look at the equation in that form and tell about\r\n" );
document.write( "the graph easier. You can just look at the equation and\r\n" );
document.write( "pick out the radius and the center without doing any\r\n" );
document.write( "algebra.   \r\n" );
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document.write( "The two red 2's tell you the center is (2,2) and the green 4 tells you\r\n" );
document.write( "that the radius is 4, so you can draw it in your head.\r\n" );
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document.write( "On top of that, it IS the equation of that circle because the\r\n" );
document.write( "points (-2,2), (2,-2), (2,6), (6,2) all lie on this circle\r\n" );
document.write( "as you can see:\r\n" );
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document.write( "Plug each into \r\n" );
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document.write( "Plugging in (-2,2)\r\n" );
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document.write( "Plugging in (2,-2)\r\n" );
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document.write( "Plugging in (2,6)\r\n" );
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document.write( "Plugging in (6,2)\r\n" );
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document.write( "So you see that all those four sample points\r\n" );
document.write( "satisfy the equation in standard form. That\r\n" );
document.write( "convinces us that it must be the right\r\n" );
document.write( "equation for that circle.\r\n" );
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document.write( "Edwin
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