document.write( "Question 625489: 16x^2 + 25y^2 - 96x - 200y + 144 = 0 \r
\n" ); document.write( "\n" ); document.write( "find the center, foci, and vertices \n" ); document.write( "
Algebra.Com's Answer #393617 by lwsshak3(11628)\"\" \"About 
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16x^2 + 25y^2 - 96x - 200y + 144 = 0
\n" ); document.write( "find the center, foci, and vertices
\n" ); document.write( "**
\n" ); document.write( "16x^2 + 25y^2 - 96x - 200y + 144 = 0
\n" ); document.write( "complete the squares:
\n" ); document.write( "16(x^2-6x+9)+25(y^2-8y+16)=-144+144+400
\n" ); document.write( "16(x-3)^2+25(y-4)^2=400
\n" ); document.write( "(x-3)^2/25+(y-4)^2/16=1
\n" ); document.write( "This is an equation of an ellipse with horizontal major axis.
\n" ); document.write( "Its standard form of equation: (x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k)=(x,y) coordinates of the center.
\n" ); document.write( "For given ellipse:
\n" ); document.write( "center: (3,4)
\n" ); document.write( "a^2=25
\n" ); document.write( "a=√25=5
\n" ); document.write( "vertices: (3±a,4)=(3±5,4)=(-2,4) and (8,4)
\n" ); document.write( "..
\n" ); document.write( "b^2=16
\n" ); document.write( "b=4
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2-b^2=25-16=9
\n" ); document.write( "c=√9=3
\n" ); document.write( "Foci: (3±c,4)=(3±3,4)=(0,4) and (6,4) \n" ); document.write( "
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