document.write( "Question 920285: Identify the following conic. That is, is it a circle, parabola, hyperbola or ellipse? Show why? \r
\n" ); document.write( "\n" ); document.write( "x^2-4y^2-4x-24y=48 \n" ); document.write( "
Algebra.Com's Answer #558284 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Here's how you tell just by looking at the equation, assuming there are no xy terms:\r\n" );
document.write( "\r\n" );
document.write( "Circle -- 2nd degree polynomial equation having both x² and y² terms with the\r\n" );
document.write( "same COEFFICIENT when on the same side of the equation.\r\n" );
document.write( "\r\n" );
document.write( "Parabola -- 2nd degree polynomial equation having only an x² term or a y² term\r\n" );
document.write( "but not both.\r\n" );
document.write( "\r\n" );
document.write( "Hyperbola -- 2nd degree polynomial equation having both x² and y² terms with\r\n" );
document.write( "OPPOSITE SIGNS when on the same side of the equation.\r\n" );
document.write( "\r\n" );
document.write( "Ellipse -- 2nd degree polynomial equation having both x² and y² terms with\r\n" );
document.write( "DIFFERENT COEFFICIENTS BUT BOTH WITH THE SAME SIGN when on the same side of the\r\n" );
document.write( "equation.\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "x²-4y²-4x-24y=48\r\n" );
document.write( "\r\n" );
document.write( "That's a polynomial equation having both x² and y² terms with OPPOSITE SIGNS\r\n" );
document.write( "when on the same side of the equation.  So it's a HYPERBOLA.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );