document.write( "Question 475138: I need be able to find the center, vertices, and foci of the ellipse with the equation 4x2 + y2 - 8x + 4y - 8 = 0.. I can't seem to get it right! \n" ); document.write( "
Algebra.Com's Answer #325802 by lwsshak3(11628)\"\" \"About 
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I need be able to find the center, vertices, and foci of the ellipse with the equation 4x2 + y2 - 8x + 4y - 8 = 0.. I can't seem to get it right!I need be able to find the center, vertices, and foci of the ellipse with the equation 4x2 + y2 - 8x + 4y - 8 = 0.. I can't seem to get it right!
\n" ); document.write( "**
\n" ); document.write( "f(x)=4x2+y2-8x+4y-8=0
\n" ); document.write( "completing the squares
\n" ); document.write( "4(x^2-2x+1)+(y^2+4y+4)-8-4-4=0
\n" ); document.write( "4(x-1)^2+(y+2)^2=16
\n" ); document.write( "divide by 16
\n" ); document.write( "(x-1)^2/4+(y+2)^2/16=1
\n" ); document.write( "This is an ellipse with vertical major axis of standard form: (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( "Center:(1,-2)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=4
\n" ); document.write( "length of major axis=2a=8
\n" ); document.write( "vertices: (1,-2±a)=(1,-2±4)=(1,-6) and (1,2)
\n" ); document.write( "..
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2-b^2=16-4=12
\n" ); document.write( "c√12
\n" ); document.write( "Foci: (1,-2±c)=(1,-2±√12)=(1,1.46) and (1,-5.46) \n" ); document.write( "
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