document.write( "Question 152653: Complete the square and write the equation in standard form. Then give the center and radius of the circle.
\n" ); document.write( "x2 + y2 - 2x - 4y - 4 = 0
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Algebra.Com's Answer #112291 by mducky2(62) $\"\"$ $\"About$

You can put this solution on YOUR website!
It's easier to start by separating the x's from the y's:
\n" ); document.write( " $\"x%5E2+%2B+y%5E2+-+2x+-+4y+-+4+=+0\"$
\n" ); document.write( " $\"%28x%5E2+-+2x%29+%2B+%28y%5E2+-+4y%29+-+4+=+0\"$
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In order to complete the square, we can use this equation:
\n" ); document.write( " $\"x%5E2+%2B+bx+%2B+%28b%2F2%29%5E2+=+%28x+%2B+b%2F2%29%5E2\"$
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Now let's make the x's fit into this equation:
\n" ); document.write( " $\"x%5E2+-+2x\"$
\n" ); document.write( "We know that b = -2. But make sure to subtract whatever you add on so that everything adds up back in the original formula:
\n" ); document.write( " $\"x%5E2+-+2x+%2B+1%5E2+-+1%5E2\"$
\n" ); document.write( " $\"x%5E2+-+2x+%2B+1+-+1\"$
\n" ); document.write( " $\"%28x+%2B+1%29%5E2+-+1\"$
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Now let's make the y's fit into this equation:
\n" ); document.write( " $\"y%5E2+-+4y\"$
\n" ); document.write( "We know that b = -4
\n" ); document.write( " $\"y%5E2+-+4y+%2B+2%5E2+-+2%5E2\"$
\n" ); document.write( " $\"y%5E2+-+4y+%2B+4+-+4\"$
\n" ); document.write( " $\"%28y+-+4%29%5E2+-+4\"$
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Putting everything back into the original equation, we can now write it in standard form:
\n" ); document.write( " $\"%28x%5E2+-+2x%29+%2B+%28y%5E2+-+4y%29+-+4+=+0\"$
\n" ); document.write( " $\"%28%28x+%2B+1%29%5E2+-+1%29+%2B+%28%28y+-+4%29%5E2+-+4%29+-+4+=+0\"$
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Moving all the excess numbers to the side:
\n" ); document.write( " $\"%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+-+4+-+1+-+4+=+0\"$
\n" ); document.write( " $\"%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+-+9+=+0\"$
\n" ); document.write( " $\"%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+=+9\"$
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The center of a circle (h,k) and the radius r can be found using this equation:
\n" ); document.write( " $\"%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2\"$
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Back to the equation:
\n" ); document.write( " $\"%28x+%2B+1%29%5E2+%2B+%28y+-+4%29%5E2+=+9\"$
\n" ); document.write( "It looks like h = -1 and k = 4. Therefore the center of the circle is (-1,4).
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It also looks like r² = 9. Let's solve for r:
\n" ); document.write( " $\"r%5E2+=+9\"$
\n" ); document.write( " $\"r+=+3\"$
\n" ); document.write( "Therefore, the radius of the circle is 3.\r
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