document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826098>Question 826098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the equation of the hyperbola whose vertices are the foci of the ellipse 11x^2 + 7y^2 + 14y - 70 = 0 and its foci are the vertices of the given ellipse.\r<BR>\n" );
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document.write( "thanks :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497920 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=497920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> determine the equation of the hyperbola whose vertices are the foci of the ellipse 11x^2 + 7y^2 + 14y - 70 = 0 and its foci are the vertices of the given ellipse. <BR>\n" );
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document.write( "11x^2 + 7y^2 + 14y - 70 = 0<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "11x^2+7(y^2+2y+1)=70+7=77<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F7%2B%28y%2B1%29%5E2%2F11=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F7%2B%28y%2B1%29%5E2%2F11=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of an ellipse with vertical major axis.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "For given equation of th ellipse:<BR>\n" );
document.write( "center:(0,-1)<BR>\n" );
document.write( "a^2=11<BR>\n" );
document.write( "a=&#8730;11&#8776;3.32<BR>\n" );
document.write( "vertices: (0,-1±a)=(0,-1±&#8730;11)=(0,-1±3.32)=(0,-4.32)and(=(0,+2.32)<BR>\n" );
document.write( "b^2=7<BR>\n" );
document.write( "b=&#8730;7<BR>\n" );
document.write( "c^2=a^2-b^2=11-7=4<BR>\n" );
document.write( "c=±2<BR>\n" );
document.write( "foci:(0,-1±c)=(0,-1±2)=(0,-3)and(=(0,+1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given hyperbola:<BR>\n" );
document.write( "assume same center as given ellipse: (0,-1)<BR>\n" );
document.write( "Hyperbola has a vertical transverse axis:<BR>\n" );
document.write( "Its standard form of equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=2(foci of ellipse)<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "c^2=11(vertex of ellipse)<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "b^2=c^2-a^2=11-4=7<BR>\n" );
document.write( "Equation of given hyperbola:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2%2F4-x%5E2%2F7=1 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2%2F4-x%5E2%2F7=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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