document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=455268>Question 455268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^2-y^2+6x+10y-17=0\r<BR>\n" );
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document.write( "A.) Write the equation in standard form.<BR>\n" );
document.write( "B.) Find the Center, Verticies, Foci, and slope of asymptotes.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313114 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=313114\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2-y^2+6x+10y-17=0 <BR>\n" );
document.write( "A.) Write the equation in standard form.<BR>\n" );
document.write( "B.) Find the Center, Verticies, Foci, and slope of asymptotes.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of a hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of a hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between the two forms is the interchange of (x-h) and (y-k)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x^2-y^2+6x+10y-17=0<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "(x^2+6x+9)-(y^2-10y+25)=17+9+25=51<BR>\n" );
document.write( "(x+3)^2/51-(y-5)^2/51=1<BR>\n" );
document.write( "This is a hyperbola with horizontal transverse axis (first form listed above).<BR>\n" );
document.write( "center:(-3,5)<BR>\n" );
document.write( "a^2=51<BR>\n" );
document.write( "a=&#8730;51=7.1..<BR>\n" );
document.write( "vertices: (-3±&#8730;51,5)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=51<BR>\n" );
document.write( "b=&#8730;51<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=51+51=102<BR>\n" );
document.write( "c=&#8730;(102)=10.1..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "foci: (-3±&#8730;(102),5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "asymptotes<BR>\n" );
document.write( "slope=±b/a=±&#8730;51/&#8730;51=±1<BR>\n" );
document.write( "Equation of asymptotes<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "y=±x+b<BR>\n" );
document.write( "solving for b using coordinates of center which are on the asymptotes<BR>\n" );
document.write( "5=±3+b<BR>\n" );
document.write( "b=8 and 2<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "y=-x+2<BR>\n" );
document.write( "y=x+8<BR>\n" );
document.write( "See graph below as a visual check on the answers<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=((x+3)^2-51)^.5+5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C+%28%28x%2B3%29%5E2-51%29%5E.5%2B5%2C-%28%28x%2B3%29%5E2-51%29%5E.5%2B5%2C-x%2B2%2Cx%2B8%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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