document.write( "Question 817915: Name the coordinates of the four vertices, the two foci, and the equations of the major and minor axes for the ellipse 25x^2+4y^2-150x+32y+189=0 \n" ); document.write( "
Algebra.Com's Answer #492370 by lwsshak3(11628)\"\" \"About 
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Name the coordinates of the four vertices, the two foci, and the equations of the major and minor axes for the ellipse
\n" ); document.write( "25x^2+4y^2-150x+32y+189=0
\n" ); document.write( "rearrange terms:
\n" ); document.write( "25x^2-150x+4y^2+32y=-189
\n" ); document.write( "complete the square:
\n" ); document.write( "25(x^2-6x+9)+4(y^2+8y+16)=-189+225+64
\n" ); document.write( "25(x-3)^2+4(y+4)^2=100
\n" ); document.write( "\"%28x-3%29%5E2%2F4%2B%28y%2B4%29%5E2%2F25=1\"
\n" ); document.write( "This is an equation of an ellipse with vertical major axis
\n" ); document.write( "Its standard form of equation:
\n" ); document.write( "\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\",a>b, (h,k)=(x,y) coordinates of center
\n" ); document.write( "..
\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,-4±a)=(3,-4±5)=(3,-9) and (3,1)(ends of major axis)
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "vertices:(3±b,-4)=(3±2,-4)=(1,-4) and (5,-4)(ends of minor axis)
\n" ); document.write( "c^2=a^2-b^2=25-4=21
\n" ); document.write( "c=√21≈4.6
\n" ); document.write( "foci:(3,-4±c)=(3,-4±4.6)=(3,-8.6) and (3,.6)\r
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