document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83616>Question 83616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the conic(cirlce, ellipse, hyperbola, ellipse. Write each of the following in standard form. Find the information listed for each problem. Graph the equation.\r<BR>\n" );
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document.write( "1) x^2+y^2-16x+12y=0\r<BR>\n" );
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document.write( "What is it?_________<BR>\n" );
document.write( "Center_________<BR>\n" );
document.write( "Radius__________<BR>\n" );
document.write( "Standard Form_________ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60135 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=60135\">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=1+%2A+x+%5E+2+%2B+y+%5E+2+-+1+6+%2A+x+%2B+1+2+%2A+y++=0 ALIGN=MIDDLE  ALT=\"1+%2A+x+%5E+2+%2B+y+%5E+2+-+1+6+%2A+x+%2B+1+2+%2A+y++=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given conic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+x+%5E+2+-+1+6+%2A+x+%29+%2B+%28+y+%5E+2+%2B+1+2+%2A+y+%29+=+0+++++ ALIGN=MIDDLE  ALT=\"%28+x+%5E+2+-+1+6+%2A+x+%29+%2B+%28+y+%5E+2+%2B+1+2+%2A+y+%29+=+0+++++\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "Now we must complete the individual squares inside the parenthesis:\r<BR>\n" );
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document.write( " For instance to complete <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%28+x+%5E+2+-+1+6+%2A+x+%29+ ALIGN=MIDDLE  ALT=\"1+%28+x+%5E+2+-+1+6+%2A+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, take half of -16 and square it (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16%2F2%29%5E2=%28-8%29%5E2=64 ALIGN=MIDDLE  ALT=\"%28-16%2F2%29%5E2=%28-8%29%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 64. Now add 64 inside the parenthesis like this: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+x+%5E+2+-+1+6+%2A+x+%2B+6+4+%29+ ALIGN=MIDDLE  ALT=\"%28+x+%5E+2+-+1+6+%2A+x+%2B+6+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since you really added <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A64 ALIGN=MIDDLE  ALT=\"1%2A64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the entire left side, we must add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A64 ALIGN=MIDDLE  ALT=\"1%2A64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right side also. Now lets complete  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+%5E+2+%2B+1+2+%2A+y+%29 ALIGN=MIDDLE  ALT=\"+%28+y+%5E+2+%2B+1+2+%2A+y+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In order to complete <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+y+%5E+2+%2B+1+2+%2A+y+%29 ALIGN=MIDDLE  ALT=\"%28+y+%5E+2+%2B+1+2+%2A+y+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, take half of 12 and square it (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F2%29%5E2=%286%29%5E2=36 ALIGN=MIDDLE  ALT=\"%2812%2F2%29%5E2=%286%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 36. Now add 36 inside the parenthesis like this: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+%5E+2+%2B+1+2+%2A+y+%2B+3+6+%29 ALIGN=MIDDLE  ALT=\"+%28+y+%5E+2+%2B+1+2+%2A+y+%2B+3+6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since you really added <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A36 ALIGN=MIDDLE  ALT=\"1%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the entire left side, we must add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A36 ALIGN=MIDDLE  ALT=\"1%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right side also.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+%5E+2+-+1+6+%2A+x+%2B+6+4+%29+%2B+%28+y+%5E+2+%2B+1+2+%2A+y+%2B+3+6+%29+=+-+0+%2B+6+4+%2A+1+%2B+3+6+%2A+1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the individual squares by taking half of the 2nd coefficient and squaring it (remember to add to both sides).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+%5E+2+-+1+6+%2A+x+%2B+6+4+%29+%2B+%28+y+%5E+2+%2B+1+2+%2A+y+%2B+3+6+%29+=+1+0+0+ ALIGN=MIDDLE  ALT=\"+%28+x+%5E+2+-+1+6+%2A+x+%2B+6+4+%29+%2B+%28+y+%5E+2+%2B+1+2+%2A+y+%2B+3+6+%29+=+1+0+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+8+%29+%5E+2+%2B++%28+y+%2B+6+%29+%5E+2+=+1+0+0+ ALIGN=MIDDLE  ALT=\"+%28+x+-+8+%29+%5E+2+%2B++%28+y+%2B+6+%29+%5E+2+=+1+0+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the individual groups on the left side.\r<BR>\n" );
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document.write( "So the equation is now in standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where (h,k) is the center and r is the radius\r<BR>\n" );
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document.write( "So the equation is a circle with a radius of 10 and a center of (8,-6)\r<BR>\n" );
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document.write( "Here's the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+x+-+8+%29+%5E+2+%2B+%28+y+%2B+6+%29+%5E+2+=+1+0+0+ ALIGN=MIDDLE  ALT=\"%28+x+-+8+%29+%5E+2+%2B+%28+y+%2B+6+%29+%5E+2+=+1+0+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28500%2C500%2C-20%2C+20%2C+-20%2C+20%2C%0D%0A+++circle%288%2C-6%2C10%29%2C%0D%0A+++circle%288%2C-6%2C0.08%29%2C%0D%0A+++circle%288%2C-6%2C0.10%29%2C%0D%0A+++graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C0%29%0D%0A+++%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What is it? Circle<BR>\n" );
document.write( "Center: (8,-6)<BR>\n" );
document.write( "Radius: 10<BR>\n" );
document.write( "Standard Form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+x+-+8+%29+%5E+2+%2B+%28+y+%2B+6+%29+%5E+2+=+1+0+0+ ALIGN=MIDDLE  ALT=\"%28+x+-+8+%29+%5E+2+%2B+%28+y+%2B+6+%29+%5E+2+=+1+0+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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