document.write( "Question 946148: If variable point (x, y) satisfies the equation x2 + y2 – 8x – 6y + 9 = 0, then range of y/x is \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "answers is [-7/24 , infinity) \n" ); document.write( "

Algebra.Com's Answer #577237 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2%2By%5E2-8x-6y%2B9=0\"$
\n" ); document.write( " $\"%28x%5E2-8x%29%2B%28y%5E2-6y%29=-9\"$
\n" ); document.write( " $\"%28x%5E2-8x%2B16%29%2B%28y%5E2-6y%2B9%29=-9%2B16%2B9\"$
\n" ); document.write( " $\"%28x-4%29%5E2%2B%28y-3%29%5E2=16\"$
\n" ); document.write( " $\"%28y-3%29%5E2=16-%28x-4%29%5E2\"$
\n" ); document.write( " $\"y-3=+0+%2B-+sqrt%2816-%28x-4%29%29%5E2\"$
\n" ); document.write( " $\"y=-3+%2B-+sqrt%2816-%28x-4%29%29%5E2\"$
\n" ); document.write( "Now you can look at the values of $\"Z=y%2Fx\"$
\n" ); document.write( " $\"Z=%28-3+%2B-+sqrt%2816-%28x-4%29%5E2%29%29%2Fx\"$
\n" ); document.write( "Since Z is now the function of only one variable, take the derivative and set it equal to zero to find the maximum value.
\n" ); document.write( "We'll do it in two parts because of the plus/minus value.
\n" ); document.write( " $\"Z%5B1%5D=%28-3+%2B+sqrt%2816-%28x-4%29%5E2%29%29%2Fx\"$
\n" ); document.write( " $\"Z%5B1%5D\"$ has a minimum of $\"y%2Fx=3%2F8\"$ when $\"x=8\"$ .
\n" ); document.write( " $\"Z%5B2%5D=%28-3+-+sqrt%2816-%28x-4%29%5E2%29%29%2Fx\"$
\n" ); document.write( " $\"Z%5B2%5D\"$ has a minimum of $\"y%2Fx=-7%2F24\"$ when $\"x=72%2F25\"$ .
\n" ); document.write( "There is no maximum so the range of $\"y%2Fx\"$ is [ $\"-7%2F24\"$ , $\"infinity\"$ )
\n" ); document.write( " \n" ); document.write( "

\n" );