document.write( "Question 461591: Find the center, vertices and foci of the ellipse 32x^2+4y^2+192x-24y=-196 \n" ); document.write( "
Algebra.Com's Answer #316527 by lwsshak3(11628)\"\" \"About 
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Find the center, vertices and foci of the ellipse 32x^2+4y^2+192x-24y=-196
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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( "32x^2+4y^2+192x-24y=-196
\n" ); document.write( "completing the square
\n" ); document.write( "32(x^2+6x+9)+4(y^2-6y+9)=-196+288+36=128
\n" ); document.write( "32(x+3)^2+4(y-3)^2=128
\n" ); document.write( "divide by 128
\n" ); document.write( "(x+3)^2/4+(y-3)^2/32=1
\n" ); document.write( "Because the y-term has the larger denominator, this ellipse has a vertical major axis, second form listed above.
\n" ); document.write( "center: (-3,3)
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\n" ); document.write( "a^2=32
\n" ); document.write( "a=√32=5.66
\n" ); document.write( "length of major axis=2a=2√32
\n" ); document.write( "vertices: (3,3±a)=(3,3±√32)
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\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "length of minor axis=2b=4
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\n" ); document.write( "c^2=a^2-b^2=32-4=28
\n" ); document.write( "c=√28=5.29..
\n" ); document.write( "Foci:(3,3±c)=(3,3±√28)
\n" ); document.write( "See the graph below as a visual check on the answers
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\n" ); document.write( "\n" ); document.write( "y= (32-8(x+3)^2)^.5+3 \r
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