document.write( "Question 877742: center: (2,15)
\n" ); document.write( "point on circle: (5,15)
\n" ); document.write( "write the equation of each circle with the given information. then write the equation of the line tangent to the circle at the given point. (Hint: You will need both length and slope of the radius.) \n" ); document.write( "

Algebra.Com's Answer #529531 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the radius by using the distance between the center and the point.
\n" ); document.write( " $\"R%5E2=%282-5%29%5E2%2B%2815-15%29%5E2\"$
\n" ); document.write( " $\"R%5E2=%28-3%29%5E2\"$
\n" ); document.write( " $\"R=3\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"%28x-2%29%5E2%2B%28y-15%29%5E2=9\"$
\n" ); document.write( "Take the derivative to find the slope of the tangent line at any point,
\n" ); document.write( " $\"2%28x-2%29%2B2%28y-15%29=0\"$
\n" ); document.write( " $\"%282x-4%29dx%2B%282y-30%29dy=0\"$
\n" ); document.write( " $\"%282y-30%29dy=%284-2x%29dx\"$
\n" ); document.write( " $\"dy%2Fdx=%284-2x%29%2F%282y-30%29\"$
\n" ); document.write( " $\"m=dy%2Fdx=%282-x%29%2F%28y-15%29\"$
\n" ); document.write( "At $\"x=5\"$ ,
\n" ); document.write( " $\"m=%282-5%29%2F%2815-15%29\"$
\n" ); document.write( "The slope is infinite at that point.
\n" ); document.write( " $\"x=5\"$ is the tangent.
\n" ); document.write( "

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

\n" );