document.write( "Question 203603: please helppppppp:
\n" ); document.write( "Find the equation of circle with centre (6,7) and tangent to the line 5x-20y+24=0 \n" ); document.write( "

Algebra.Com's Answer #153660 by scott8148(6628) $\"\"$ $\"About$

You can put this solution on YOUR website!
a tangent is perpendicular to the radius at the point of tangency
\n" ); document.write( "___ so you need to find the distance from the point to the line, to find the radius of the circle
\n" ); document.write( "___ you already have the center, so the equation is (x-6)^2 + (y-7)^2 = r^2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "5x + 24 = 20y ___ (1/4)x + 6/5 = y ___ the slope of the given line is 1/4\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so the slope of the radius line (perpendicular) is -4\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "equation of radius line ___ (y - 7) = -4 (x - 6) ___ y = -4x + 31\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substituting to find intersection ___ x/4 + 6/5 = -4x + 31\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "clearing fractions ___ 5x + 24 = -80x + 620 ___ 85x = 644 ___ x = 644/85\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "substituting ___ y = (1/4)(644/85) + 6/5 ___ y = 263/85\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "using the distance formula ___ r^2 = [6 - (644/85)]^2 + [7 - (263/85)]^2 = (-134/85)^2 + (332/85)^2 = 1508/85 \n" ); document.write( "

\n" );