document.write( "Question 531363: Classify the conic section of the equation 4x2 + 9y2 - 8x - 18y - 19 = 0. \n" ); document.write( "

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Classify the conic section of the equation 4x2 + 9y2 - 8x - 18y - 19 = 0.
\n" ); document.write( "**
\n" ); document.write( "4x2 + 9y2 - 8x - 18y - 19 = 0.
\n" ); document.write( "complete the square
\n" ); document.write( "4(x^2-2x+1)+9(y^2-2y+1)=19+4+9=32
\n" ); document.write( "4(x-1)^2+9(y-1)^2=32
\n" ); document.write( "Divide both sides by 32
\n" ); document.write( "(x-1)^2/(32/4)+9(y-1)^2/(32/9)=1
\n" ); document.write( "(x-1)^2/8+(y-1)^2/(32/9)=1
\n" ); document.write( "This an equation of an ellipse with horizontal major axis of the standard form:
\n" ); document.write( "(x-h)^2/a^2+(y-k^2)/b^2=1, a>b, with (h,k) being (x,y) coordinates of the center
\n" ); document.write( "For given equation:
\n" ); document.write( "Center: (1,1)
\n" ); document.write( "a^2=8
\n" ); document.write( "b^2=32/9 \n" ); document.write( "

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