document.write( "Question 1085731: Decide whether or not the equation has a circle as its graph. If it does, give the center
\n" ); document.write( "and the radius. If it does not, describe the graph.\r
\n" ); document.write( "\n" ); document.write( "x^2+y^2+6x−10y+38=0 \n" ); document.write( "

Algebra.Com's Answer #699816 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2By%5E2%2B6x%26%238722%3B10y%2B38=0+\"$ ...to check if it is a circle, write the equation in form $\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B6x%2By%5E2-10y=-38\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B6x%29%2B%28y%5E2-10y%29=-38\"$ ...............complete squares\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B6x%2Bb%5E2%29+-b%5E2%2B%28y%5E2-10y%2Bb%5E2%29+-b%5E2+=-38\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B6x%2B3%5E2%29+-3%5E2%2B%28y%5E2-10y%2B5%5E2%29+-5%5E2+=-38\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%29%5E2+-9%2B%28y-5%29%5E2+-25+=-38\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%29%5E2+%2B%28y-5%29%5E2++=-38%2B34\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%29%5E2+%2B%28y-5%29%5E2++=+-4\"$ -> negative number shows us it is $\"not\"$ a circle\r
\n" ); document.write( "\n" ); document.write( "and the equation $\"does\"$ $\"+not\"$ match the form of $\"any\"$ $\"+conic\"$ section\r
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