document.write( "Question 1008349: what is the value of k in x^2+y^2-6x+8y+5=k in a circle, a point, and an empty set? please answer. \n" ); document.write( "

Algebra.Com's Answer #624985 by Fombitz(32388) $\"\"$ $\"About$

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Complete the square.
\n" ); document.write( " $\"x%5E2-6x%2By%5E2%2B8y=k-5\"$
\n" ); document.write( " $\"%28x%5E2-6x%2B9%29%2B%28y%5E2%2B8y%2B16%29-9-16=k-5\"$
\n" ); document.write( " $\"%28x-3%29%5E2%2B%28y%2B4%29%5E2=k%2B20\"$
\n" ); document.write( "If the right hand side is greater than zero, then it is the square of the radius of the circle centered at (3,-4).
\n" ); document.write( " $\"k%2B20%3E0\"$
\n" ); document.write( " $\"k%3E-20\"$
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\n" ); document.write( "If the right hand side is equal to zero, then it is a single point, namely the center (3,-4).
\n" ); document.write( " $\"k%2B20=0\"$
\n" ); document.write( " $\"k=-20\"$
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\n" ); document.write( "If the right hand side is less than zero, then the solution is the empty set.
\n" ); document.write( " $\"k%3C-20\"$ \n" ); document.write( "

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