document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=597522>Question 597522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm so lost on parabola and hyperbola and don't know where to start on these problems \r<BR>\n" );
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document.write( "1) (y-3)^2-4(x-4)^2=16\r<BR>\n" );
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document.write( "it is asking for the standard form of this equation, center, vertices, foci ,asymptotes  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378290 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=378290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (y-3)^2-4(x-4)^2=16 <BR>\n" );
document.write( "it is asking for the standard form of this equation, center, vertices, foci ,asymptotes<BR>\n" );
document.write( "**<BR>\n" );
document.write( "(y-3)^2-4(x-4)^2=16 <BR>\n" );
document.write( "divide by16<BR>\n" );
document.write( "(y-3)^2/16-(x-4)^2/4=1<BR>\n" );
document.write( "This is an equation of a hyperbola with vertical transverse axis (y-term comes first) of the 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-3)^2/16-(x-4)^2/4=1<BR>\n" );
document.write( "center: (4,3)<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=&#8730;16=4<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "b=&#8730;4=2<BR>\n" );
document.write( "c^2=a^2+b^2=16+4=20<BR>\n" );
document.write( "c=&#8730;20&#8776;4.5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "vertices: (4,3±a)=(4,3±4)=(4,-1) and (4,7)<BR>\n" );
document.write( "foci: (4,3±c)=(4,3±4.5)=(4,-1.5) and (4,7.5)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes are straight lines of the standard form y=mx+b, m=slope, b=y-intercept.<BR>\n" );
document.write( "Asymptotes also go thru the center.<BR>\n" );
document.write( "slope of asymptotes=±a/b=±4/2=±2<BR>\n" );
document.write( "Equations of asymptotes:<BR>\n" );
document.write( "y=2x+b<BR>\n" );
document.write( "solving for b using coordinates of center which are on the line<BR>\n" );
document.write( "3=2*4+b<BR>\n" );
document.write( "b=-5<BR>\n" );
document.write( "equation: y=2x-5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=-2x+b<BR>\n" );
document.write( "solving for b using coordinates of center which are on the line<BR>\n" );
document.write( "3=-2*4+b<BR>\n" );
document.write( "b=11<BR>\n" );
document.write( "equation: y=-2x+11\r<BR>\n" );
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