document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=874125>Question 874125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the center, vertices, foci and equations of the asymptotes \r<BR>\n" );
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document.write( "(X-5)^2 OVER 4 -  (Y+2)^2 OVER 16 =1 \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527381 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=527381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> determine the center, vertices, foci and equations of the asymptotes <BR>\n" );
document.write( "(X-5)^2 OVER 4 - (Y+2)^2 OVER 16 =1 <BR>\n" );
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document.write( "(x-5)^2/4-(y+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 of equation: ((x-h)^2/b^2-(y-k)^2/a^2=1}}}, (h,k)=coordinates of center<BR>\n" );
document.write( "For given hyperbola:<BR>\n" );
document.write( "center: (5-2)<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=4<BR>\n" );
document.write( "vertices: (5±a,-2)=(5±4,-2)=(-1,-2) and (9,-2)<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "c^2=a^2+b^216+4=20<BR>\n" );
document.write( "c=&#8730;20&#8776;4.5<BR>\n" );
document.write( "foci: (5±c,-2)=(5±4.5,-2)=(-1.5,-2) and (9.5,-2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "The two asymptotes are straight line equations that go through the center (5,-2), and take the form y=mx+b, m=slope, b=y-intercept.<BR>\n" );
document.write( "slopes of asymptotes for hyperbolas with vertical transverse axis=±a/b=±4/2=±2<BR>\n" );
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document.write( "For asymptote with negative slope: <BR>\n" );
document.write( "y=-2x+b<BR>\n" );
document.write( "solve for b using coordinates of the center<BR>\n" );
document.write( "-2=-2*5+b<BR>\n" );
document.write( "b=8<BR>\n" );
document.write( "equation:y=-2x+8<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For asymptote with positive slope: <BR>\n" );
document.write( "y=2x+b<BR>\n" );
document.write( "solve for b using coordinates of the center<BR>\n" );
document.write( "-2=2*5+b<BR>\n" );
document.write( "b=-12<BR>\n" );
document.write( "equation:y=2x-12\r<BR>\n" );
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