document.write( "Question 310361: Find an equation of the line tangent to the circle (x − 9)^2 + (y − 2)^2 = 25 at the point (12, −2) \n" ); document.write( "

Algebra.Com's Answer #221903 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's use implicit differentiation to find the derivative at that point.
\n" ); document.write( " $\"%28x-9%29%5E2%2B%28y-2%29%5E2=25\"$
\n" ); document.write( "Differentiating,
\n" ); document.write( " $\"2%28x-9%29dx%2B2%28y-2%29dy=0\"$
\n" ); document.write( " $\"%28y-2%29dy=%289-x%29dx\"$
\n" ); document.write( " $\"dy%2Fdx=%289-x%29%2F%28y-2%29\"$
\n" ); document.write( "The value of the derivative equals the slope of the tangent line at that point.
\n" ); document.write( "So at (12,-2),
\n" ); document.write( " $\"dy%2Fdx=%289-12%29%2F%28-2-2%29\"$
\n" ); document.write( " $\"dy%2Fdx=-3%2F-4=3%2F4\"$
\n" ); document.write( "Use the point-slope form of a line,
\n" ); document.write( " $\"y-yp=m%28x-xp%29\"$
\n" ); document.write( " $\"y-%28-2%29=%283%2F4%29%28x-12%29\"$
\n" ); document.write( " $\"y%2B2=%283%2F4%29x-9\"$
\n" ); document.write( " $\"y=%283%2F4%29x-11\"$
\n" ); document.write( "

\n" ); document.write( "

\n" );