document.write( "Question 1099107: derive the equation of a circle which passes through the point(-2,1), its tangent to the line 3x-2y-6=0 at the point (4,3) \n" ); document.write( "

Algebra.Com's Answer #713585 by Edwin McCravy(20083) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Here's a better way.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We set the lengths of the two green radii equal:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That simplifies to:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's one equation in h and k.\r\n" );
document.write( "\r\n" );
document.write( "To get the other equation in h and k, we use the fact that a \r\n" );
document.write( "tangent to a circle is perpendicular to the radius drawn to the \r\n" );
document.write( "point of tangency.\r\n" );
document.write( "\r\n" );
document.write( "We find the slope of the tangent line:\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( "Comparing that to y = mx+b, the tangent line has slope\r\n" );
document.write( " so the radius drawn to the point of tangency\r\n" );
document.write( "has slope , its \"negative reciprocal\".\r\n" );
document.write( "\r\n" );
document.write( "So we use the slope formula and set its slope equal to \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That simplifies to:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we solve this system:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Solve that by substitution or elimination and get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we find the length of the radius, using the distance\r\n" );
document.write( "formula for the length of the radius drawn to the point \r\n" );
document.write( "of tangency:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which simplifies to \r\n" );
document.write( "\r\n" );
document.write( "Substituting for the center and radius in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which simplifies to:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );