document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615541>Question 615541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you find the vertices, co-vertices, foci, and asymptotes of:\r<BR>\n" );
document.write( "\n" );
document.write( "9(x+2)^2 -16(y-1)^2=-144 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387248 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=387248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do you find the vertices, co-vertices, foci, and asymptotes of: <BR>\n" );
document.write( "9(x+2)^2 -16(y-1)^2=-144<BR>\n" );
document.write( "divide by -144<BR>\n" );
document.write( "-(x+2)^2/16+(y-1)^2/9=1<BR>\n" );
document.write( "(y-1)^2/9-(x+2)^2/16=1<BR>\n" );
document.write( "This is an equation of a hyperbola with vertical transverse axis.<BR>\n" );
document.write( "Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "For given equation: (y-1)^2/9-(x+2)^2/16=1<BR>\n" );
document.write( "center: (-2,1)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "vertices:(-2,1±a)=(-2,1±3)=(-2,-2) and (-2,4)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "co-vertices:(-2±b,1)=(-2±4,1)=(-6,1) and (2,1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=9+16=25<BR>\n" );
document.write( "c=&#8730;25=5<BR>\n" );
document.write( "foci::(-2,1±c)=(-2,1±5)=(-2,-4) and (-2,6)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes are straight lines that intersect at the center<BR>\n" );
document.write( "slopes of asymptotes=±a/b=±3/4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with negative slope<BR>\n" );
document.write( "y=mx+b, m=slope, b=intercept<BR>\n" );
document.write( "y=-3x/4+b<BR>\n" );
document.write( "Solve for b using coordinates of center<BR>\n" );
document.write( "1=-3*-2/4+b<BR>\n" );
document.write( "b=1-6/4=-2/4=-1/2<BR>\n" );
document.write( "Equation: y=-3x/4-1/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with positive slope<BR>\n" );
document.write( "y=mx+b, m=slope, b=intercept<BR>\n" );
document.write( "y=3x/4+b<BR>\n" );
document.write( "Solve for b using coordinates of center<BR>\n" );
document.write( "1=3*-2/4+b<BR>\n" );
document.write( "b=1+6/4=10/4=5/2<BR>\n" );
document.write( "Equation: y=3x/4+5/2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );