document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288643>Question 288643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Classify the conic section. (State whether it is a hyperbola, ellipse, circle or parabola). Be sure to use correct spelling or your answer will be marked wrong. 16x^2 + 9y^2 + 24x - 36y + 23 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "Also my teacher said that this problem couldnt be an ellipse because I originally thought thats what this was but unfortunately its not so thats why I'm confused, please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209203 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=209203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+ ALIGN=MIDDLE  ALT=\"16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+%2B+9y%5E2+%2B+24x+-+36y++=+-23+ ALIGN=MIDDLE  ALT=\"16x%5E2+%2B+9y%5E2+%2B+24x+-+36y++=+-23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 23 from both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E2%2B+24x%29+%2B+%289y%5E2++-+36y%29+=+-23+ ALIGN=MIDDLE  ALT=\"%2816x%5E2%2B+24x%29+%2B+%289y%5E2++-+36y%29+=+-23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x%5E2%2B+%283%2F2%29x%29+%2B+9%28y%5E2++-+4y%29+=+-23+ ALIGN=MIDDLE  ALT=\"16%28x%5E2%2B+%283%2F2%29x%29+%2B+9%28y%5E2++-+4y%29+=+-23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading terms from each group (to make their coefficients equal to 1).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x%5E2%2B+%283%2F2%29x%2B9%2F4-9%2F4%29+%2B+9%28y%5E2++-+4y%2B4-4%29+=+-23+ ALIGN=MIDDLE  ALT=\"16%28x%5E2%2B+%283%2F2%29x%2B9%2F4-9%2F4%29+%2B+9%28y%5E2++-+4y%2B4-4%29+=+-23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for each group (let me know if you need help with that)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28%28x%5E2%2B+%283%2F2%29x%2B9%2F16%29-9%2F16%29+%2B+9%28%28y%5E2++-+4y%2B4%29-4%29+=+-23+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Group the first three terms in each group.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28%28x%5E2%2B3%2F4%29%5E2-9%2F16%29+%2B+9%28%28y-2%29%5E2-4%29+=+-23+ ALIGN=MIDDLE  ALT=\"16%28%28x%5E2%2B3%2F4%29%5E2-9%2F16%29+%2B+9%28%28y-2%29%5E2-4%29+=+-23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor each grouped trinomial.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x%5E2%2B3%2F4%29%5E2-9+%2B+9%28y-2%29%5E2-36+=+-23+ ALIGN=MIDDLE  ALT=\"16%28x%5E2%2B3%2F4%29%5E2-9+%2B+9%28y-2%29%5E2-36+=+-23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x%5E2%2B3%2F4%29%5E2+%2B+9%28y-2%29%5E2-45+=+-23+ ALIGN=MIDDLE  ALT=\"16%28x%5E2%2B3%2F4%29%5E2+%2B+9%28y-2%29%5E2-45+=+-23+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x%5E2%2B3%2F4%29%5E2+%2B+9%28y-2%29%5E2+=+-23%2B45+ ALIGN=MIDDLE  ALT=\"16%28x%5E2%2B3%2F4%29%5E2+%2B+9%28y-2%29%5E2+=+-23%2B45+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 45 to both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x%5E2%2B3%2F4%29%5E2+%2B+9%28y-2%29%5E2+=+22+ ALIGN=MIDDLE  ALT=\"16%28x%5E2%2B3%2F4%29%5E2+%2B+9%28y-2%29%5E2+=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%28x%5E2%2B3%2F4%29%5E2%29%2F22+%2B+%289%28y-2%29%5E2%29%2F22+=+1+ ALIGN=MIDDLE  ALT=\"%2816%28x%5E2%2B3%2F4%29%5E2%29%2F22+%2B+%289%28y-2%29%5E2%29%2F22+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide every term outside the parenthesis by 22 to make the right side equal to 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+ ALIGN=MIDDLE  ALT=\"%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+ ALIGN=MIDDLE  ALT=\"%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-h%29%5E2%29%2F%28a%5E2%29+%2B+%28%28y-k%29%5E2%29%2F%28b%5E2%29+=+1+ ALIGN=MIDDLE  ALT=\"%28%28x%5E2-h%29%5E2%29%2F%28a%5E2%29+%2B+%28%28y-k%29%5E2%29%2F%28b%5E2%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-3%2F4 ALIGN=MIDDLE  ALT=\"h=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=22%2F16 ALIGN=MIDDLE  ALT=\"a%5E2=22%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=22%2F9 ALIGN=MIDDLE  ALT=\"b%5E2=22%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-h%29%5E2%29%2F%28a%5E2%29+%2B+%28%28y-k%29%5E2%29%2F%28b%5E2%29+=+1+ ALIGN=MIDDLE  ALT=\"%28%28x%5E2-h%29%5E2%29%2F%28a%5E2%29+%2B+%28%28y-k%29%5E2%29%2F%28b%5E2%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the general equation of an ellipse. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+ ALIGN=MIDDLE  ALT=\"%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an ellipse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+ ALIGN=MIDDLE  ALT=\"%28%28x%5E2%2B3%2F4%29%5E2%29%2F%2822%2F16%29+%2B+%28%28y-2%29%5E2%29%2F%2822%2F9%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+ ALIGN=MIDDLE  ALT=\"16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+ ALIGN=MIDDLE  ALT=\"16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is also an ellipse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+ ALIGN=MIDDLE  ALT=\"16x%5E2+%2B+9y%5E2+%2B+24x+-+36y+%2B+23+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an ellipse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So either there's a typo or your teacher is mistaken. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );