document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572346>Question 572346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve and graph this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x%5E2-4y%5E2%2B18x%2B32y-91=0+ ALIGN=MIDDLE  ALT=\"+9x%5E2-4y%5E2%2B18x%2B32y-91=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I tried putting it in standard form and it ended up being a horizontal hyperbola. The standard form was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B2%29%5E2+%2F+7+-+4%28y%2B4%29%5E2+%2F+63+=+1+ ALIGN=MIDDLE  ALT=\"+%28x%2B2%29%5E2+%2F+7+-+4%28y%2B4%29%5E2+%2F+63+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From there I got the center of the hyperbola which is (h,k) or (-2,-4)and I graphed it. Then I looked for the values for a, b, and c. A was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt+%28+7+%29+ ALIGN=MIDDLE  ALT=\"+sqrt+%28+7+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 2.6 as a decimal and B was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt+%28+63+%29+ ALIGN=MIDDLE  ALT=\"+sqrt+%28+63+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 7.9 as a decimal. I graphed A and B as the conjugate and transverse axes. This is where I got confused. The equation for the hyperbola had x on the left and y on the right, meaning it should graph horizontally. But I graphed the axes and the hyperbola came out vertical. Please help me see where I went wrong! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368435 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=368435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve and graph<BR>\n" );
document.write( "9x^2-4y^2+18x+32y-91=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "9(x^2+2x+1)-4(y^2-8y+16)=91+9-64=36<BR>\n" );
document.write( "9(x+1)^2-4(y-4)^2=36<BR>\n" );
document.write( "(x+1)^2/4-(y-4)^2/9=1<BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis of the standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "Center:(-1,4)<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "slope of asymptotes=±b/a=±3/2<BR>\n" );
document.write( "Equation of asymptotes:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=-3x/2+b<BR>\n" );
document.write( "solving for b using (x,y) coordinates of center thru which the asymptote goes.<BR>\n" );
document.write( "4=-(3*-1)/2+b<BR>\n" );
document.write( "b=5/2<BR>\n" );
document.write( "Equation:y=-3x/2+5/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=3x/2+b<BR>\n" );
document.write( "solving for b using (x,y) coordinates of center thru which the asymptote goes.<BR>\n" );
document.write( "4=(3*-1)/2+b<BR>\n" );
document.write( "b=11/2<BR>\n" );
document.write( "Equation:y=3x/2+11/2<BR>\n" );
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document.write( "see the graph below as a visual check on the above:<BR>\n" );
document.write( "y=(2.25(x+1)^2-9)^.5+4<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%282.25%28x%2B1%29%5E2-9%29%5E.5%2B4%2C-%282.25%28x%2B1%29%5E2-9%29%5E.5%2B4%2C-3x%2F2%2B5%2F2%2C3x%2F2%2B11%2F2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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