document.write( "Question 1185705: Find the equation of the circle that passes through the point (9,7) and is tangent to both x and y axis and the line 3x-4y=24 \n" ); document.write( "

Algebra.Com's Answer #816550 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "There are too many constraints; no circle satisfies all of them.

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

\n" ); document.write( "The graph of the line 3x-4y=24 lies in quadrants I, III, and IV.
\n" ); document.write( "To be tangent to both the x- and y-axes, the center of the circle must be on either the line y=x or the line y=-x.
\n" ); document.write( "So tangent to both the x- and y-axes and to the line 3x-4y=24, there is one circle in quadrant I, one in quadrant IV, and two in quadrant III.
\n" ); document.write( "None of them passes through the given point (9,7).

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

\n" ); document.write( "To be tangent to both the x- and y-axes, the center of the circle must be on either the line y=x or the line y=-x.
\n" ); document.write( "The given point (9,7) is in quadrant I, so the circle needs to be in quadrant I.
\n" ); document.write( "There are two circles in quadrant I that are tangent to the x- and y-axes and pass through (9,7).
\n" ); document.write( "Neither of them is tangent to the line 3x-4y=24.

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

\n" );