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find the center,vertices and foci of the ellipse:
\n" ); document.write( "16x^2+4y^2+64x-24y+36=0
\n" ); document.write( "**
\n" ); document.write( "16x^2+4y^2+64x-24y+36=0
\n" ); document.write( "complete the squares:
\n" ); document.write( "16(x^2+4x+4)+4(y^2-6y+9)=-36+64+36=64
\n" ); document.write( "16(x+2)^2+4(y-3)^2=64
\n" ); document.write( "divide by 64
\n" ); document.write( "(x+2)^2/4+(y-3)^2/16=1
\n" ); document.write( "This is an ellipse with a vertical major axis of the standard form:
\n" ); document.write( "(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( "..
\n" ); document.write( "For given problem:
\n" ); document.write( "Center: (-2,3)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=√16=4
\n" ); document.write( "length of vertical major axis=2a=8
\n" ); document.write( "vertices: (end-points of major axis)=(-2, 3±a)=(-2, 3±4)=(-2,7) and (-2,-1)
\n" ); document.write( "Vertices: (-2,7) and (-2,-1)
\n" ); document.write( "..
\n" ); document.write( "b^2=4
\n" ); document.write( "b=√4=2
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2-b^2=16-4=12
\n" ); document.write( "c=√12=3.46
\n" ); document.write( "Foci: (-2,3±c)=(-2,3±3.46)=(-2, 6.46) and (-2, -.46)
\n" ); document.write( "Ans:
\n" ); document.write( "Center: (-2,3)
\n" ); document.write( "Vertices: (-2,7) and (-2,-1)
\n" ); document.write( "Foci:(-2, 6.46) and (-2, -.46)\r
\n" ); document.write( "\n" ); document.write( "See graph below as a visual check on answers:
\n" ); document.write( "..
\n" ); document.write( "y=±((16-4(x+2)^2)^.5)+3
\n" ); document.write( "