document.write( "Question 751026: what conic section is (x-3)^2-y^2=1 considered?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #456944 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
what conic section is (x-3)^2-y^2=1 considered?
\n" ); document.write( "

Rule:\r\n" );
document.write( "\r\n" );
document.write( "1. Get it in the general form\r\n" );
document.write( "\r\n" );
document.write( "Ax² + Bxy + Cy² + Dx + Ey + F = 0,\r\n" );
document.write( "\r\n" );
document.write( "2. Calculate the discriminant B²-4AC\r\n" );
document.write( "\r\n" );
document.write( "3.  if discriminant = 0, the graph is a parabola\r\n" );
document.write( "    if discriminant < 0, the graph is an ellipse\r\n" );
document.write( "    if discriminant < 0 and A=C then it is a special ellipse,\r\n" );
document.write( "                                          that is, a CIRCLE! \r\n" );
document.write( "\r\n" );
document.write( "    if discriminant > 0, hyperbola \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply it out and get it in general order:\r\n" );
document.write( "\r\n" );
document.write( "x² - 6x + 9 - y² = 1\r\n" );
document.write( "\r\n" );
document.write( "x² - y² - 6x + 8 = 0\r\n" );
document.write( "\r\n" );
document.write( "The general order for all conic sections is\r\n" );
document.write( "\r\n" );
document.write( "Ax² + Bxy + Cy² + Dx + Ey + F = 0, so we write ours as:\r\n" );
document.write( "\r\n" );
document.write( "1x² + 0xy - 1y² - 6x + 0y + 8 = 0\r\n" );
document.write( "\r\n" );
document.write( "A=1, B=0, C=-1, D=-6, E=0, F=8\r\n" );
document.write( "\r\n" );
document.write( "We calculate discriminant = B²-4AC\r\n" );
document.write( "                            0²-4(1)(-1)\r\n" );
document.write( "                            0+4\r\n" );
document.write( "                            4\r\n" );
document.write( "\r\n" );
document.write( "That's > 0 so the graph is a hyperbola.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );