document.write( "Question 420767: what is the graphic equation of? 4x2 + 9y2 - 16x -126y + 421 \n" ); document.write( "
Algebra.Com's Answer #294318 by lwsshak3(11628)\"\" \"About 
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what is the graphic equation of? 4x2 + 9y2 - 16x -126y + 421\r
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\n" ); document.write( "\n" ); document.write( "To find out which conic equation this is, you need to complete the square.\r
\n" ); document.write( "\n" ); document.write( "4x2+9y2-16x-126y+421
\n" ); document.write( "=4x^2-16x+9y^2-126y=-421
\n" ); document.write( "=4(x^2-4x+4)+9(y^2-14y+49)=-421+16+441=36
\n" ); document.write( "=4(x-2)^2+9(y-7)^2=36
\n" ); document.write( "divide by 36
\n" ); document.write( "=(x-2)^2/9+(y-7)^2/4=1
\n" ); document.write( "Standard form of an ellipse:(x-h)^2/a^2+(y-k)^2/b=1, with (h,k) being the (x,y) coordinates of the center. Length of major axis=2a. Length of minor axis=2b. Length of vertices=sqrt(a^2-b^2)
\n" ); document.write( "From this equation, you should see that the equation is an ellipse with center at (2,7) and a horizontal major axis.
\n" ); document.write( "See the graph below:\r
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\n" ); document.write( "y=7+-(4-4(x-2)^2/9)^.5\r
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