document.write( "Question 1094135: find the equation of two circles which pass through point (2, 0) that have both Y-axis and the line y-1 =0 as the tangent.\r
\n" ); document.write( "\n" ); document.write( "am sorry to asked this question but I need your help.
\n" ); document.write( "thank \n" ); document.write( "

Algebra.Com's Answer #708768 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Let the radius be r,\r\n" );
document.write( "\r\n" );
document.write( "Then the x-coordinate of the center is the length of the\r\n" );
document.write( "radius from the y-axis, so it is r.\r\n" );
document.write( "\r\n" );
document.write( "The y-coordinate of the center is r units below the line\r\n" );
document.write( "y-1 = 0, which is the same as y = 1, a horizontal line\r\n" );
document.write( "1 unit above and parallel to the x-axis, in red.\r\n" );
document.write( "\r\n" );
document.write( "The y-coordinate of the center is 5 units below the red line.\r\n" );
document.write( "Since the red line is 1 unit above the x-axis, we need to\r\n" );
document.write( "subtract the radius from 1 to get the y-coordinate, That's\r\n" );
document.write( "1-r, so that's the y-coordinate of the center, and the \r\n" );
document.write( "center is (r,1-r).   \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "The center is (r,r-1) and the radius is r\r\n" );
document.write( "so the equation of the circle, \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "becomes:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and since it goes through (2,0)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "r-1 = 0;   r-5 = 0\r\n" );
document.write( "  r = 1      r = 5\r\n" );
document.write( "\r\n" );
document.write( "The small circle has r=1, center (r,1-r) = (1,1-1) = (1,0)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and the large circle has r=5, center (r,1-r) = (5,1-5) = (5,-4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );