document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=817914>Question 817914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Name the coordinates of the two vertices,the two foci, and find the equations of the asymptotes for the hyperbola 16x^2-y^2+96x+8y+112=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492378 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=492378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Name the coordinates of the two vertices,the two foci, and find the equations of the asymptotes for the hyperbola <BR>\n" );
document.write( "16x^2-y^2+96x+8y+112=0<BR>\n" );
document.write( "rearrange terms:<BR>\n" );
document.write( "16x^2+96x-y^2+8y=-112<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "16(x^2+6x+9)-(y^2-8y+16)=-112+144-16<BR>\n" );
document.write( "16(x+3)^2-(y-4)^2=16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2F1-%28y-4%29%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2F1-%28y-4%29%5E2%2F16=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( "center:(-3,4)<BR>\n" );
document.write( "a^2=1<BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "vertices: (-3±a,4)=(-3±1,4)=(-4,4) and (-2,4)<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "b=&#8730;16=4<BR>\n" );
document.write( "c^2=a^2+b^2=1+4=5<BR>\n" );
document.write( "c=&#8730;5&#8776;2.2<BR>\n" );
document.write( "Foci:(-3±c,4)=(-3±2.2,4)=(-5.2,4) and (-.8,4)<BR>\n" );
document.write( "slopes of asymptotes with horizontal transverse axis=±b/a=±4/1=±4<BR>\n" );
document.write( "asymptotes are equations of straight lines that go through the center(-3,4)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "asymptote with positive slope:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=4x+b<BR>\n" );
document.write( "solve for b using coordinates of center which are on the line.<BR>\n" );
document.write( "4=4*(-3)+b<BR>\n" );
document.write( "b=16<BR>\n" );
document.write( "equation:y=4x+16<BR>\n" );
document.write( "..<BR>\n" );
document.write( "asymptote with negative slope:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=-4x+b<BR>\n" );
document.write( "solve for b using coordinates of center which are on the line.<BR>\n" );
document.write( "4=-4*(-3)+b<BR>\n" );
document.write( "b=-8<BR>\n" );
document.write( "equation:y=-4x-8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );