document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204698>Question 1204698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the equation of the hyperbola in standard form and general form.<BR>\n" );
document.write( "https://i.ibb.co/4jjgzVK/1.jpg\r<BR>\n" );
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document.write( "Answer for the standard equation was ((y + 1)^2)/4  -  ((x + 2)^2)/(1/4) = 1\r<BR>\n" );
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document.write( "My answer was of course wrong: ((y + 1)^2)/16  -  ((x + 2)^2)/1 = 1<BR>\n" );
document.write( "There was no point in rewriting into general form when my standard form was already incorrect\r<BR>\n" );
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document.write( "What I did:<BR>\n" );
document.write( "Center (-2, -1)<BR>\n" );
document.write( "I picked points (-1, 3) and (-3, 3) on the two asymptotes to find slope +/- 4<BR>\n" );
document.write( "Does that mean a = 4 and b = 1?<BR>\n" );
document.write( "Because that’s what I used to plug into the equation ((y - k)^2)/a^2  -  ((x - h)^2)/b^2 = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841133 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The slopes of the asymptotes being 4 and -4 does not mean a=4 and b=1.  It only means a/b=4.<br><BR>\n" );
document.write( "The given graph shows the larger y value when x=-2 has to be 1.  Use that to find a and then b:<br><BR>\n" );
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document.write( "(revised presentation, after question from student....)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2%2Fa%5E2-%28x%2B2%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2%2Fa%5E2-%28x%2B2%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When x = -2, the y value is 1:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B1%29%5E2%2Fa%5E2-%28-2%2B2%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%281%2B1%29%5E2%2Fa%5E2-%28-2%2B2%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%5E2%2Fa%5E2-%280%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%282%29%5E2%2Fa%5E2-%280%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"4%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=4 ALIGN=MIDDLE  ALT=\"a%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then a/b=4 leads to b=1/2.<br><BR>\n" );
document.write( "That gives you the correct equation.<br><BR>\n" );
document.write( " </SPAN>\n" );
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