document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176576>Question 1176576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the standard form of the equation of the hyperbola with the given characteristics.\r<BR>\n" );
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document.write( "Foci: (±10, 0); asymptotes: y = ±4/3x<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803731 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  \r<BR>\n" );
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document.write( "There are two standard forms:\r<BR>\n" );
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document.write( "   1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1%7D%7D%0D%0A%0D%0A%0D%0AThe+point-slope+form+for+the+equations+of+the+asymptotes+is%3A%0D%0A%0D%0A%7B%7B%7By ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >= ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%28x-h%29%2Bk ALIGN=MIDDLE  ALT=\"+m%28x-h%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29x ALIGN=MIDDLE  ALT=\"%284%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  tell us that h=0 and k=0 <BR>\n" );
document.write( " The center is the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "Foci is  given to be, (±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), tells us that the hyperbola is the horizontal transverse type with the equation in item 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2Fa%5E2-%28y-0%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2Fa%5E2-%28y-0%29%5E2%2Fb%5E2=1\"   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=x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The distance to the focus is linear eccentricity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The point (10, 0)  shows us the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=10 ALIGN=MIDDLE  ALT=\"c=10\"   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=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   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=y+ ALIGN=MIDDLE  ALT=\"y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29x ALIGN=MIDDLE  ALT=\"%284%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > shows us that\r<BR>\n" );
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document.write( "-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fa=4%2F3 ALIGN=MIDDLE  ALT=\"b%2Fa=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4a%2F3 ALIGN=MIDDLE  ALT=\"b=4a%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2=a%5E2%2B%284a%2F3%29%5E2 ALIGN=MIDDLE  ALT=\"10%5E2=a%5E2%2B%284a%2F3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=a%5E2%2B16a%5E2%2F9 ALIGN=MIDDLE  ALT=\"100=a%5E2%2B16a%5E2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=25a%5E2%2F9 ALIGN=MIDDLE  ALT=\"100=25a%5E2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900%2F25=a%5E2 ALIGN=MIDDLE  ALT=\"900%2F25=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=a%5E2 ALIGN=MIDDLE  ALT=\"36=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F6=4%2F3 ALIGN=MIDDLE  ALT=\"b%2F6=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=24%2F3 ALIGN=MIDDLE  ALT=\"b=24%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8 ALIGN=MIDDLE  ALT=\"b=8\"   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=x%5E2%2F6%5E2-y%5E2%2F8%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F6%5E2-y%5E2%2F8%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and your equation in standard form is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36-y%5E2%2F64=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36-y%5E2%2F64=1\"   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%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C%0D%0Acircle%2810%2C0%2C.12%29%2Ccircle%28-10%2C0%2C.12%29%2C%0D%0Alocate%2810%2C0.7%2CF%2810%2C0%29%29%2Clocate%28-10%2C0.7%2CF%28-10%2C0%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C-%284%2F3%29x+%2C%284%2F3%29x%2Csqrt%2864%28-1%2Bx%5E2%2F36%29%29%2C+-sqrt%2864%28-1%2Bx%5E2%2F36%29%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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