document.write( "Question 974686: The graph of the equation x^2 + y^2 + 8x − 10y − 40 = 0 is which of the following conic sections?\r
\n" ); document.write( "\n" ); document.write( "A. parabola\r
\n" ); document.write( "\n" ); document.write( "B. hyperbola\r
\n" ); document.write( "\n" ); document.write( "C. ellipse\r
\n" ); document.write( "\n" ); document.write( "D. circle \n" ); document.write( "
Algebra.Com's Answer #596534 by htmentor(1343)\"\" \"About 
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If we rearrange the equation, grouping the x and y terms, and move the constant term to the other side, we have:
\n" ); document.write( "x^2 + 8x + y^2 - 10y = 40
\n" ); document.write( "Complete the squares:
\n" ); document.write( "(1) (x+4)^2 = x^2 + 8x + 16
\n" ); document.write( "(2) (y-5)^2 = y^2 - 10y + 25
\n" ); document.write( "Since the constant terms add to 41, we need to subtract this from the LHS in order to write the equation as the sum of (1) and (2):
\n" ); document.write( "x^2 + 8x + y^2 - 10y -> (x+4)^2 + (y-5)^2 - 41 = 40 -> (x+4)^2 + (y-5)^2 = 81
\n" ); document.write( "This is the equation for a circle with center (-4,5), and radius sqrt(81) = 9
\n" ); document.write( "Graph is shown below.
\n" ); document.write( "Ans: D circle
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