document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081571>Question 1081571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3, 5).\r<BR>\n" );
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document.write( "Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695631 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=695631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a hyperbola with foci at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and vertices at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >). \r<BR>\n" );
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document.write( "determine if it is<BR>\n" );
document.write( "horizontal:  <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;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "vertical:  <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 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2+-+%28x-h%29%5E2%2Fb%5E2+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To start, let's graph the information we have:\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+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%283%2C-3%2C.12%29%2Ccircle%283%2C7%2C.12%29%2Ccircle%283%2C-1%2C.12%29%2Ccircle%283%2C5%2C.12%29%2C%0D%0Alocate%283%2C-3%2Cf%283%2C-3%29%29%2Clocate%283%2C7%2Cf%283%2C7%29%29%2Clocate%283%2C-1%2Cv%283%2C-1%29%29%0D%0A%2Clocate%283%2C5%2Cv%283%2C5%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,you have vertical:  \r<BR>\n" );
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document.write( "<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 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2+-+%28x-h%29%5E2%2Fb%5E2+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now<BR>\n" );
document.write( "1. Identify the center point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "it is midpoint of line segment:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"%283%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2B7%29%2F2 ALIGN=MIDDLE  ALT=\"%28-3%2B7%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "The center point is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "so,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" >\r<BR>\n" );
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document.write( "put it on a graph:\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+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%283%2C-3%2C.12%29%2Ccircle%283%2C7%2C.12%29%2Ccircle%283%2C-1%2C.12%29%2Ccircle%283%2C5%2C.12%29%2Ccircle%283%2C2%2C.12%29%2C%0D%0Alocate%283%2C-3%2Cf%283%2C-3%29%29%2Clocate%283%2C7%2Cf%283%2C7%29%29%2Clocate%283%2C-1%2Cv%283%2C-1%29%29%0D%0A%2Clocate%283%2C5%2Cv%283%2C5%29%29%2Clocate%283%2C2%2CC%283%2C2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. Identify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we'll count from the center to either vertex; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+3 ALIGN=MIDDLE  ALT=\"a+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we'll count from the center to either focus;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+5 ALIGN=MIDDLE  ALT=\"+c+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. Use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%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=b%5E2=c%5E2+-a%5E2+ ALIGN=MIDDLE  ALT=\"b%5E2=c%5E2+-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=b%5E2=5%5E2+-3%5E2+ ALIGN=MIDDLE  ALT=\"b%5E2=5%5E2+-3%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=25+-9+ ALIGN=MIDDLE  ALT=\"b%5E2=25+-9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=16+ ALIGN=MIDDLE  ALT=\"b%5E2=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4. Plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   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=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the correct pattern.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%5E2%2F3%5E2+-+%28x-3%29%5E2%2F4%5E2+=1 ALIGN=MIDDLE  ALT=\"%28y-2%29%5E2%2F3%5E2+-+%28x-3%29%5E2%2F4%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=%28y-2%29%5E2%2F9+-+%28x-3%29%5E2%2F16+=1 ALIGN=MIDDLE  ALT=\"%28y-2%29%5E2%2F9+-+%28x-3%29%5E2%2F16+=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+-20%2C+20%2C+-20%2C+20%2C%0D%0Acircle%283%2C-3%2C.12%29%2Ccircle%283%2C7%2C.12%29%2Ccircle%283%2C-1%2C.12%29%2Ccircle%283%2C5%2C.12%29%2Ccircle%283%2C2%2C.12%29%2C%0D%0Alocate%283%2C-3%2Cf%283%2C-3%29%29%2Clocate%283%2C7%2Cf%283%2C7%29%29%2Clocate%283%2C-1%2Cv%283%2C-1%29%29%0D%0A%2Clocate%283%2C5%2Cv%283%2C5%29%29%2Clocate%283%2C2%2CC%283%2C2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+20%2Csqrt%289%28x-3%29%5E2%2F16+%2B9%29%2B2%2C-sqrt%289%28x-3%29%5E2%2F16+%2B9%29%2B2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "next problem is of same type; so,I am pretty sure you can do it following these steps\r<BR>\n" );
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document.write( " </SPAN>\n" );
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