document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=692052>Question 692052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you kindly help with the following problem\r<BR>\n" );
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document.write( "Draw the hyperbolas and the eccentricity of the following:\r<BR>\n" );
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document.write( "4x^2 - 9y^2 - 16x + 18y = 29\r<BR>\n" );
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document.write( "I having a hard time getting into the hyperbola standard equation\r<BR>\n" );
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document.write( "Regards,<BR>\n" );
document.write( "Gheomell </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427078 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=427078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw the hyperbolas and the eccentricity of the following: <BR>\n" );
document.write( "4x^2 - 9y^2 - 16x + 18y = 29<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "4x^2-16x-9y^2+18y=29<BR>\n" );
document.write( "4(x^2-4x+4)-9(y^2-2y+1)=29+16-9<BR>\n" );
document.write( "4(x-2)^2-9(y-1)^2=36<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2F9-%28y-1%29%5E2%2F4=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F9-%28y-1%29%5E2%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis.<BR>\n" );
document.write( "Its standard form of equation: <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;\" >, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "For given equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2F9-%28y-1%29%5E2%2F4=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F9-%28y-1%29%5E2%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "center: (2,1)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=&#8730;9=3<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "b=&#8730;4=2<BR>\n" );
document.write( "c^2=a^2+b^2=9+4=13<BR>\n" );
document.write( "c=&#8730;13<BR>\n" );
document.write( "eccentricity=c/a=&#8730;13/3 (there is no graph for this)<BR>\n" );
document.write( "see graph below<BR>\n" );
document.write( "y=±(4(x-2)^2/9-4)^.5+1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%284%28x-2%29%5E2%2F9-4%29%5E.5%2B1%2C-%284%28x-2%29%5E2%2F9-4%29%5E.5%2B1%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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