document.write( "Question 877943: Analyze the Conic Section (center, vertices intercepts ...)\r
\n" ); document.write( "\n" ); document.write( "(4x^2)+(9y^2)-40x+64 = 0
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #529636 by lwsshak3(11628)\"\" \"About 
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Analyze the Conic Section (center, vertices intercepts ...)
\n" ); document.write( "(4x^2)+(9y^2)-40x+64 = 0
\n" ); document.write( "4x^2-40x+9y^2=-64
\n" ); document.write( "complete the square
\n" ); document.write( "4(x^2-10x+25)+9y^2=-64+100
\n" ); document.write( "4(x-5)^2+9y^2=36
\n" ); document.write( "\"%28x-5%29%5E2%2F9%2By%5E2%2F4=1\"
\n" ); document.write( "This is an equation of an ellipse with horizontal major axis
\n" ); document.write( "Its standard form of equation: \"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\", a>b, (h,k)=coordinates of center
\n" ); document.write( "For given ellipse:
\n" ); document.write( "center: (5,0)
\n" ); document.write( "a^2=9
\n" ); document.write( "a=3
\n" ); document.write( "length of major axis=2a=6
\n" ); document.write( "vertices: (5±a,0)=(5±3,0)=(2,0) and(8,0)
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "length of minor axis=2b=4
\n" ); document.write( "x-intercept:
\n" ); document.write( "set y=0
\n" ); document.write( "(x-5)^2/9=1
\n" ); document.write( "(x-5)^2=9
\n" ); document.write( "x-5=±√9=±3
\n" ); document.write( "x=5±3
\n" ); document.write( "x-intercept=2, 8
\n" ); document.write( "..
\n" ); document.write( "y-intercept
\n" ); document.write( "set x=0
\n" ); document.write( "(-5)^2/9+y^2/4=1
\n" ); document.write( "y^2/4=1-25/9=-16/9
\n" ); document.write( "y^2=-64/9
\n" ); document.write( "y-intercept: none\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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