document.write( "Question 1192295: The graph of $(x-3)^2 + (y-5)^2=16$ is reflected over the line $y=2$. The new graph is the graph of the equation $x^2 + Bx + y^2 + Dy + F = 0$ for some constants $B$, $D$, and $F$. Find $B+D+F$. \n" ); document.write( "

Algebra.Com's Answer #824216 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The center of the given circle is (3,5) and the radius is 4.

\n" ); document.write( "The reflection in the line y=2 moves the center of the circle; the radius stays the same.

\n" ); document.write( "The center of the circle is 3 units above the line of reflection, so the center of the new circle is 3 units below; the new center is (3,-1).

\n" ); document.write( "The equation of the new circle is (x-3)^2+(y+1)^2=16.

\n" ); document.write( " $\"%28x-3%29%5E2%2B%28y%2B1%29%5E2=16\"$
\n" ); document.write( " $\"x%5E2-6x%2B9%2By%5E2%2B2y%2B1=16\"$
\n" ); document.write( " $\"x%5E2-6x%2By%5E2%2B2y-6=0\"$

\n" ); document.write( "B+D+F = (-6)+(2)+(-6) = -10

\n" ); document.write( "ANSWER: -10

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