document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=531225>Question 531225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hyperbola with its Center (-3,2), transverse axis parallel to the y-axis, passing through (1,7), the asymptotes are perpendicular to each other. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350474 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=350474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A hyperbola with its Center (-3,2), transverse axis parallel to the y-axis, passing through (1,7), the asymptotes are perpendicular to each other.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Standard form of equation for a hyperbola with vertical transverse axis, as in this case:<BR>\n" );
document.write( "(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( "..<BR>\n" );
document.write( "Took me awhile to figure out that if the asymptotes are perpendicular to each other their slopes must be equal to ±1.<BR>\n" );
document.write( "slope=a/b=±1<BR>\n" );
document.write( "so, a=b or a=-b<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Given equation:<BR>\n" );
document.write( "(y-2)^2/a^2-(x+3)^2/b^2=1<BR>\n" );
document.write( "can be rewritten:<BR>\n" );
document.write( "(y-2)^2/a^2-(x+3)^2/a^2=1<BR>\n" );
document.write( "using given point on parabola (1,7) to solve for a<BR>\n" );
document.write( "(7-2)^2/a^2-(1+3)^2/a^2=1<BR>\n" );
document.write( "25/a^2-16/a^2=1<BR>\n" );
document.write( "9/a^2=1<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "b=a=3<BR>\n" );
document.write( "Equation of given hyperbola:<BR>\n" );
document.write( "(y-2)^2/9-(x+3)^2/9=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes:<BR>\n" );
document.write( "Asymptotes are straight lines thru the center of the hyperbola of the standard form:<BR>\n" );
document.write( "y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "for slope=1<BR>\n" );
document.write( "2=1*-3+b<BR>\n" );
document.write( "b=5<BR>\n" );
document.write( "equation of asymptote<BR>\n" );
document.write( "y=x+5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "for slope=-1<BR>\n" );
document.write( "2=-1*-3+b<BR>\n" );
document.write( "b=-1<BR>\n" );
document.write( "equation of asymptote<BR>\n" );
document.write( "y=-x-1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "See graph as a visual check on answers:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=±(9+(x+3)^2)^.5+2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%289%2B%28x%2B3%29%5E2%29%5E.5%2B2%2C-%289%2B%28x%2B3%29%5E2%29%5E.5%2B2%2Cx%2B5%2C-x-1%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );