document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975429>Question 975429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the hyperbola: 9x2 – 54x – 16y2 + 64y – 127 = 0        <BR>\n" );
document.write( "                     <BR>\n" );
document.write( "    a) Put the equation in standard form.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    b) Horizontal or vertical transverse axis? \r<BR>\n" );
document.write( "\n" );
document.write( "    c) Find center, vertices, foci, and the <BR>\n" );
document.write( "        equation of both asymptotes.\r<BR>\n" );
document.write( "\n" );
document.write( "    d) Sketch a graph of this hyperbola.                    <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597221 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=597221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the hyperbola: 9x2 – 54x – 16y2 + 64y – 127 = 0 <BR>\n" );
document.write( "a) Put the equation in standard form. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2F16-%28y-2%29%5E2%2F9+=1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F16-%28y-2%29%5E2%2F9+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) Horizontal or vertical transverse axis? <BR>\n" );
document.write( "c) Find center, vertices, foci, and the <BR>\n" );
document.write( "equation of both asymptotes. <BR>\n" );
document.write( "d) Sketch a graph of this hyperbola.<BR>\n" );
document.write( "***<BR>\n" );
document.write( "9x^2 – 54x – 16y^2 + 64y – 127 = 0 <BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "9(x^2–6x+9)–16(y^2-4y+4) = 127+81-64<BR>\n" );
document.write( "9(x-3)^2–16(y-2)^2 =144<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2F16-%28y-2%29%5E2%2F9+=1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F16-%28y-2%29%5E2%2F9+=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)=coordinates of center<BR>\n" );
document.write( "center: (3, 2)<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=4<BR>\n" );
document.write( "vertices: (3ħa, 2)=(3ħ4, 2)=(-1, 2) and (7, 2)<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "c^2=a^2+b^2=16+9=25<BR>\n" );
document.write( "c=5<BR>\n" );
document.write( "foci: (3ħc, 2)=(3ħ5, 2)=(-2, 2) and (8, 2)<BR>\n" );
document.write( "Asymptotes: (2 lines that intersect  and go thru center)<BR>\n" );
document.write( "slopes of asymptotes=ħb/a=ħ3/4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation of asymptote with negative slope:<BR>\n" );
document.write( "y=-3x/4+b<BR>\n" );
document.write( "solve for b using coordinates (3, 2) of center<BR>\n" );
document.write( "2=-3*3/4+b<BR>\n" );
document.write( "b=2+9/4=17/4<BR>\n" );
document.write( "equation: y=-3x/4+17/4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation of asymptote with positive slope slope:<BR>\n" );
document.write( "y=3x/4+b<BR>\n" );
document.write( "solve for b using coordinates (3, 2) of center<BR>\n" );
document.write( "2=3*3/4+b<BR>\n" );
document.write( "b=2-9/4=-1/4<BR>\n" );
document.write( "equation: y=3x/4-1/4\r<BR>\n" );
document.write( "\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=((9/16)(x-2)^2-1)^.5+2<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%28%289%2F16%29%28x-3%29%5E2-1%29%5E.5%2B2%2C-%28%289%2F16%29%28x-3%29%5E2-1%29%5E.5%2B2%2C-3x%2F4%2B17%2F4%2C3x%2F4-1%2F4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );