document.write( "Question 1079002: Find the equation of the circle that passes through (4,2) and (-6,-2), centre on the y-axis. \n" ); document.write( "

Algebra.Com's Answer #693453 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
So use the general equation of the circle,
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2\"$
\n" ); document.write( "Since you know the center is on the y-axis, then $\"h=0\"$
\n" ); document.write( " $\"x%5E2%2B%28y-k%29%5E2=R%5E2\"$
\n" ); document.write( "So using the two points,
\n" ); document.write( " $\"4%5E2%2B%282-h%29%5E2=R%5E2\"$
\n" ); document.write( " $\"16%2B%282-h%29%5E2=R%5E2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"%28-6%29%5E2%2B%28-2-h%29%5E2=R%5E2\"$
\n" ); document.write( " $\"36%2B%28-2-h%29%5E2=R%5E2\"$
\n" ); document.write( "Setting them equal to each other,
\n" ); document.write( " $\"16%2B%282-h%29%5E2=36%2B+%28-2-h%29%5E2+\"$
\n" ); document.write( " $\"16%2B4-4h%2Bh%5E2=36%2B4%2B4h%2Bh%5E2\"$
\n" ); document.write( " $\"-8h=20\"$
\n" ); document.write( " $\"h=-20%2F8\"$
\n" ); document.write( " $\"h=-5%2F2\"$
\n" ); document.write( "So then use either point to solve for R.
\n" ); document.write( " $\"16%2B%282-%28-5%2F2%29%29%5E2=R%5E2\"$
\n" ); document.write( " $\"16%2B%284%2F2%2B5%2F2%29%5E2=R%5E2\"$
\n" ); document.write( " $\"16%2B%289%2F2%29%5E2=R%5E2\"$
\n" ); document.write( " $\"64%2F4%2B81%2F4=R%5E2\"$
\n" ); document.write( " $\"R%5E2=145%2F4\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"highlight%28x%5E2%2B%28y%2B5%2F2%29%5E2=145%2F4%29\"$
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