document.write( "Question 421164: 4x^2+25y^2-8x+100y+4=0 find the center, vertices and foci of the ellipse
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Algebra.Com's Answer #294317 by lwsshak3(11628)\"\" \"About 
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4x^2+25y^2-8x+100y+4=0 find the center, vertices and foci of the ellipse
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\n" ); document.write( "Standard form of the given ellipse: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)
\n" ); document.write( "4x^2+25y^2-8x+100y+4=0
\n" ); document.write( "4x^2-8x+25y^2+100y+4=0
\n" ); document.write( "factor then complete the square
\n" ); document.write( "4(x^2-2x+1)+25(y^2+4y+4)=-4+4+100
\n" ); document.write( "4(x-1)^2+25(y+2)^2=100
\n" ); document.write( "divide by 100
\n" ); document.write( "(x-1)^2/25+(y+2)^2/4=1
\n" ); document.write( "This is an ellipse with center at(1,-2) and major axis horizontal
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\n" ); document.write( "a^2=25
\n" ); document.write( "a=5
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "c^2=a^2-b^2
\n" ); document.write( "c=sqrt(25-16)=sqrt(9)=3
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\n" ); document.write( "foci:(1+-c,-2)=(1+-3,-2)=(4,-2)and (-2,-2)
\n" ); document.write( "vertices:(1+-a,-2)=1+-5,-2)=(6,-2) and (-4,-2)\r
\n" ); document.write( "\n" ); document.write( "See graph of the ellipse below:\r
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\n" ); document.write( "y=-2+-(1-(x-1)^2/25)^.5
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