document.write( "Question 945002: I have to write the standard form equation of this circle: Three points on the circle: (-15,-9), (1,-9), and (-15,3). \n" ); document.write( "

Algebra.Com's Answer #576241 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
On the coordinate plane, the formula becomes $\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+h\"$ and $\"k\"$ are the $\"x\"$ and $\"y\"$ coordinates of the center of the circle , and $\"r\"$ is radius\r
\n" ); document.write( "\n" ); document.write( "Three points on the circle: ( $\"-15\"$ , $\"-9\"$ ), ( $\"1\"$ , $\"-9\"$ ), and ( $\"-15\"$ , $\"3\"$ ).\r
\n" ); document.write( "\n" ); document.write( "use points to find $\"+h\"$ , $\"k\"$ , and $\"r\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"$ ......for ( $\"-15\"$ , $\"-9\"$ ),\r
\n" ); document.write( "\n" ); document.write( " $\"%28-15-h%29%5E2%2B%28-9-k%29%5E2=r%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2%2B30h%2Bk%5E2%2B18k%2B306=r%5E2\"$ ............eq.1\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"$ ......for ( $\"1\"$ , $\"-9\"$ ),\r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2-2h%2B18k%2Bk%5E2%2B82=r%5E2+\"$ ............eq.2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"$ ......for ( $\"-15\"$ , $\"3\"$ ),\r
\n" ); document.write( "\n" ); document.write( " $\"%28-15-h%29%5E2%2B%283-k%29%5E2=r%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2%2B30h%2Bk%5E2-6k%2B234=r%5E2\"$ ............eq.3\r
\n" ); document.write( "\n" ); document.write( "system is:\r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2%2B30h%2Bk%5E2%2B18k%2B306=r%5E2\"$ ............eq.1
\n" ); document.write( " $\"h%5E2-2h%2B18k%2Bk%5E2%2B82=r%5E2+\"$ ............eq.2
\n" ); document.write( " $\"h%5E2%2B30h%2Bk%5E2-6k%2B234=r%5E2\"$ ............eq.3
\n" ); document.write( "----------------------------------------------------------\r
\n" ); document.write( "\n" ); document.write( "subtract eq.3 from eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2%2B30h%2Bk%5E2%2B18k%2B306-%28h%5E2%2B30h%2Bk%5E2-6k%2B234%29=r%5E2+-r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2%2B30h%2Bk%5E2%2B18k%2B306-h%5E2-30h-k%5E2%2B6k-234=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"18k%2B306%2B6k-234=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"24k%2B72=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"24k=-72\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=-72%2F24\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28k=-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2-2h%2B18k%2Bk%5E2%2B82=r%5E2+\"$ ............eq.2 substitute $\"k\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%5E2-2h%2B18%28-3%29%2B%28-3%29%5E2%2B82=r%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2-2h-54%2B9%2B82=r%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2-2h%2B37=r%5E2\"$ .............2a \r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2%2B30h%2Bk%5E2-6k%2B234=r%5E2\"$ ............eq.3 substitute $\"k\"$ and $\"r%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cross%28h%5E2%29%2B30h%2B%28-3%29%5E2-6%28-3%29%2B234=cross%28h%5E2%29-2h%2B37\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"30h%2B9%2B18%2B234=-2h%2B37\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"30h%2B261=-2h%2B37\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"30h%2B2h=-261%2B37\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"32h=-224\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h=-224%2F32\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28h=-7%29\"$ \r
\n" ); document.write( "\n" ); document.write( "go to \r
\n" ); document.write( "\n" ); document.write( " $\"h%5E2-2h%2B18k%2Bk%5E2%2B82=r%5E2+\"$ ............eq.2 substitute $\"k\"$ and $\"h\"$ and solve for $\"r\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28-7%29%5E2-2%28-7%29%2B18%28-3%29%2B%28-3%29%5E2%2B82=r%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"49%2B14-54%2B9%2B82=r%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"100=r%5E2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28r+=10%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, your equation is $\"%28x%2B7%29%5E2%2B%28y%2B3%29%5E2=100\"$ \r
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