document.write( "Question 1081947: Find the equation of a circle circumscribing the triangle determined by x-y-8=0, x=-y and y=-1. \n" ); document.write( "
Algebra.Com's Answer #696018 by ikleyn(52862)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "The line x-y-8 = 0 is perpendicular to the line x = -y.\r\n" );
document.write( "\r\n" );
document.write( "So, we have a right-angled triangle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its side y = -1 is horizontal; it represents the hypotenuse.\r\n" );
document.write( "\r\n" );
document.write( "The endpoints of the hypotenuse are \r\n" );
document.write( "\r\n" );
document.write( "     (1,-1) (intersection of  x= -y      and  y= -1),   and\r\n" );
document.write( "     (7,-1) (intersection of  x-y-8 = 0  and  y= -1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the right-angled triangle, the center of the circumscribed circle lies at the midpoint of the hypotenuse.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, in our case the center of the circumscribed circle is the point (4,-1).\r\n" );
document.write( "\r\n" );
document.write( "The radius of the circle is half-length of the hypotenuse, i.e. 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the equation of the circle is \r\n" );
document.write( "\r\n" );
document.write( "\"%28x-4%29%5E2%2B%28y-%28-1%29%29%5E2%29\" = 9    or, which is the same,\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-4%29%5E2%2B%28y%2B1%29%5E2%29\" = 9.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );