document.write( "Question 456433: 4x^2+10y^2-16x+40y+16=0 How do i find the center and foci? \n" ); document.write( "
Algebra.Com's Answer #313341 by lwsshak3(11628)\"\" \"About 
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4x^2+10y^2-16x+40y+16=0 How do i find the center and foci?
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\n" ); document.write( "4x^2+10y^2-16x+40y+16=0
\n" ); document.write( "completing the square
\n" ); document.write( "4x^2-16x+10y^2+40y=-16
\n" ); document.write( "4(x^2-4x+4)+10(y^2+4+4)=-16+16+40
\n" ); document.write( "4(x-2)^2+10(y+2)^2=40
\n" ); document.write( "(x-2)^2/10+(y+2)^2/4=40
\n" ); document.write( "This equation is an ellipse with center at (2,-2), with a horizontal major axis.
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\n" ); document.write( "Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "The difference between the two forms is the interchange of a^2 and b^2.
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\n" ); document.write( "For given equation:
\n" ); document.write( "a^2=10
\n" ); document.write( "b^2=4
\n" ); document.write( "c^2=a^2-b^2=10-4=6
\n" ); document.write( "c=√6
\n" ); document.write( "foci is at (2±√6,-2)
\n" ); document.write( "See the graph below as a visual check on the answer:\r
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\n" ); document.write( "y=(4-4(x-2)^2/10)^.5-2\r
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