document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162033>Question 162033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 20. Classify the conic section of the equation 9x^2 - 3 = 18x + 4y. \r<BR>\n" );
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document.write( "A hyperbola<BR>\n" );
document.write( "B circle<BR>\n" );
document.write( "C ellipse<BR>\n" );
document.write( "D line<BR>\n" );
document.write( "E Graph is not a conic section.<BR>\n" );
document.write( "F parabola  \r<BR>\n" );
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document.write( "I'm not sure where to start, I really would apperciate your help with how to solve this to come to the correct answer. Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119412 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=119412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Notice how there is no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term. So this means that the equation is NOT a circle, ellipse, or hyperbola. So it's either a line or a parabola. However, let's use some algebra to find out for sure.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+-+3+=+18x+%2B+4y ALIGN=MIDDLE  ALT=\"9x%5E2+-+3+=+18x+%2B+4y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+-+3-18x+=+4y ALIGN=MIDDLE  ALT=\"9x%5E2+-+3-18x+=+4y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 18x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+-18x-+3+=+4y ALIGN=MIDDLE  ALT=\"9x%5E2+-18x-+3+=+4y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=9x%5E2+-18x-+3 ALIGN=MIDDLE  ALT=\"4y=9x%5E2+-18x-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%289x%5E2+-18x-+3%29%2F4 ALIGN=MIDDLE  ALT=\"y=%289x%5E2+-18x-+3%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate \"y\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%289x%5E2%29%2F4+-%2818x%29%2F4-+%283%29%2F4 ALIGN=MIDDLE  ALT=\"y=%289x%5E2%29%2F4+-%2818x%29%2F4-+%283%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4 ALIGN=MIDDLE  ALT=\"y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So this equation fits the general second degree polynomial which means that it is a parabola. If we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4 ALIGN=MIDDLE  ALT=\"y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4 ALIGN=MIDDLE  ALT=\"y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this confirms our answer. </SPAN>\n" );
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