document.write( "Question 1008865: Let x^2 + y^2 = 10y.\r
\n" ); document.write( "\n" ); document.write( "First find
\n" ); document.write( "dy/dx
\n" ); document.write( " by implicit differentiation, simplifying the answer where reasonable. Then find an equation of the line L tangent to the graph of the given equation at the point (3, 1). \r
\n" ); document.write( "\n" ); document.write( "I got te answer x/(5-y) for dy/dx but not sure how to find the line L tangent at 3,1 \r
\n" ); document.write( "\n" ); document.write( "please explain.\r
\n" ); document.write( "\n" ); document.write( "Thnk you \n" ); document.write( "
Algebra.Com's Answer #624397 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"x%5E2%2By%5E2=10y\"\r\n" );
document.write( "\r\n" );
document.write( "\"2x%2B2y%2Aexpr%28%28dy%29%2F%28dx%29%29=10expr%28%28dy%29%2F%28dx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Divide through by 2\r\n" );
document.write( "\r\n" );
document.write( "\"x%2By%2Aexpr%28%28dy%29%2F%28dx%29%29=5expr%28%28dy%29%2F%28dx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"y%2Aexpr%28%28dy%29%2F%28dx%29%29-5expr%28%28dy%29%2F%28dx%29%29=-x\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28%28dy%29%2F%28dx%29%29%28y-5%29=-x\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28%28dy%29%2F%28dx%29%29=-x%2F%28y-5%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28%28dy%29%2F%28dx%29%29=-x%2F%28-5%2By%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28%28dy%29%2F%28dx%29%29=-x%2F%28-%285-y%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%28%28dy%29%2F%28dx%29%29=x%2F%285-y%29\"\r\n" );
document.write( "\r\n" );
document.write( "Yes you were right about the derivative.\r\n" );
document.write( "\r\n" );
document.write( "The derivative is a formula for the slope of the \r\n" );
document.write( "tangent line at the point (x,y).\r\n" );
document.write( "\r\n" );
document.write( "So the slope m of the tangent line at (3,1) is found by\r\n" );
document.write( "substituting (x,y) = (3,1) in the derivative:\r\n" );
document.write( "\r\n" );
document.write( "\"m=3%2F%285-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"m=3%2F4\"\r\n" );
document.write( "\r\n" );
document.write( "Then use the point-slope formula for a line\r\n" );
document.write( "\r\n" );
document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where (x1, y1) = (3,1)\r\n" );
document.write( "\r\n" );
document.write( "\"y-1+=+expr%283%2F4%29%28x-3%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"y-1+=+expr%283%2F4%29x-9%2F4\"\r\n" );
document.write( "\r\n" );
document.write( "\"y+=+expr%283%2F4%29x-9%2F4%2B1\"\r\n" );
document.write( "\r\n" );
document.write( "\"y+=+expr%283%2F4%29x-9%2F4%2B4%2F4\"\r\n" );
document.write( "\r\n" );
document.write( "\"y+=+expr%283%2F4%29x-5%2F4\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );