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determine the center, vertices, foci for the following ellipse.18x2+y2_108x+4y+148?
\n" ); document.write( "..
\n" ); document.write( "Standard form of ellipse for horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)
\n" ); document.write( "Standard form of ellipse for vertical major axis: (y-k)^2/a^2+(x-h)^2/b^2=1 (a>b)
\n" ); document.write( "In both forms, (h,k) represent the (x,y) coordinates of the center.
\n" ); document.write( ".. \r
\n" ); document.write( "\n" ); document.write( "18x2+y2_108x+4y+148
\n" ); document.write( "completing the squares:
\n" ); document.write( "18(x^2-6x+9)+(y^2+4y+4)=-148+162+4=18
\n" ); document.write( "divide by 18
\n" ); document.write( "(x-3)^2/1+(y+2)^2/18=1
\n" ); document.write( "change positions
\n" ); document.write( "(y+2)^2/18+(x-3)^2/1=1
\n" ); document.write( "This is an ellipse with a vertical major axis(second form described above)
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\n" ); document.write( "center: (3,-2)
\n" ); document.write( "a^2=18
\n" ); document.write( "a=sqrt(18)=4.24..
\n" ); document.write( "b=1
\n" ); document.write( "b^2=1
\n" ); document.write( "c^2=a^2-b^2=18-1=17
\n" ); document.write( "c=sqrt(17)=4.12..
\n" ); document.write( "Vertices are on the major axis on the line,x=3, -2+-4.24 or (3,2.24) and (3,-6.24)
\n" ); document.write( "Similarly, foci are on the major axis,-2+-4.12 or (3,2.12) and (3,-6.12)
\n" ); document.write( "Graph below can visually confirm the answers obtained.\r
\n" ); document.write( "\n" ); document.write( "..
\n" ); document.write( "y=+-((1-(x-3)^2)18)^.5-2
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