document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93595>Question 93595</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> please help me identify the following conic. That is, is it a circle, parabola, hyperbola or ellipse? show why please!!! x^2 - 4y^2 - 4x - 24y = 48 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68169 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=68169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4y%5E2+-+4x+-+24y+-+48+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4y%5E2+-+4x+-+24y+-+48+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Compare with the standard equation for a conic<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+2hxy+%2B+by%5E2+%2B+2gx+%2B+2fy+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+2hxy+%2B+by%5E2+%2B+2gx+%2B+2fy+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+ab+=+0 ALIGN=MIDDLE  ALT=\"h%5E2+-+ab+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then the conic is a parabola.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+ab+%3C+0 ALIGN=MIDDLE  ALT=\"h%5E2+-+ab+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then the conic is an ellipse.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+ab+%3E+0 ALIGN=MIDDLE  ALT=\"h%5E2+-+ab+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then the conic is a hyperbola.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b ALIGN=MIDDLE  ALT=\"a+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+0 ALIGN=MIDDLE  ALT=\"h+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then the conic is a circle.\r<BR>\n" );
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document.write( "Here, a = 1, b = -4, h = 0.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+ab+=+4+%3E+0 ALIGN=MIDDLE  ALT=\"h%5E2+-+ab+=+4+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and hence the conic is a hyperbola. </SPAN>\n" );
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