document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=509159>Question 509159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y^2-9x^2+2y+10=0 sketch the graoh,find the center,vertices,foci,eccentricity,asymptots. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341406 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=341406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y^2-9x^2+2y+10=0 sketch the graph,find the center,vertices,foci,eccentricity,asymptotes.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "(y^2+2y+1)-9x^2=-10+1=-9<BR>\n" );
document.write( "(y+1)^2-9x^2=-9<BR>\n" );
document.write( "divide by -9<BR>\n" );
document.write( "-(y+1)^2/9+x^2=1<BR>\n" );
document.write( "x^2-(y+1)^2/9=1<BR>\n" );
document.write( "This an equation of a hyperbola with horizontal transverse axis of the standard form:<BR>\n" );
document.write( "(x-h)^2/a^2-(y-k)^2/b^2=1<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "Center: (0,-1)<BR>\n" );
document.write( "a^2=1<BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "vertices: (0±a,-1)=(0±1,-1)=(1,-1) and (-1,-1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=9+1=10<BR>\n" );
document.write( "c=&#8730;10=3.16..<BR>\n" );
document.write( "Foci: (0±c,-1)=(0±3.16,-1)=(3.16,-1) and (-3.16,-1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Eccentricity: c/a=&#8730;10/1=&#8730;10=3.16<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes:<BR>\n" );
document.write( "slope=±b/a=±3/1=±3<BR>\n" );
document.write( "Equation: y=mx+b<BR>\n" );
document.write( "For slope=3<BR>\n" );
document.write( "y=3x+b<BR>\n" );
document.write( "find b using coordinates of center (0,-1)<BR>\n" );
document.write( "-1=3*0+b<BR>\n" );
document.write( "b=-1<BR>\n" );
document.write( "equation of asymptote: y=3x-1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For slope=-3<BR>\n" );
document.write( "y=-3x+b<BR>\n" );
document.write( "find b using coordinates of center (0,-1)<BR>\n" );
document.write( "-1=3*0+b<BR>\n" );
document.write( "b=-1<BR>\n" );
document.write( "equation of asymptote: y=-3x-1<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "Center: (0,-1)<BR>\n" );
document.write( "Vertices:(1,-1) and (-1,-1)<BR>\n" );
document.write( "Foci: (3.16,-1) and (-3.16,-1)<BR>\n" );
document.write( "Eccentricity: 3.16<BR>\n" );
document.write( "Equation of asymptotes: y=3x-1 and y=-3x-1<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=±(9x^2-9)^.5-1\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-6%2C+6%2C+-6%2C+6%2C%289x%5E2-9%29%5E.5-1%2C-%289x%5E2-9%29%5E.5-1%2C3x-1%2C-3x-1%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );