document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888443>Question 888443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the asymptotes and foci of the hyperbola described by -4x^2 +2y^2 =8 ? \r<BR>\n" );
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document.write( "What I did was:  -4x^2/8  +   2y^2/8  =  1<BR>\n" );
document.write( "Then:  -x^2/2  +  y^2/4  = 1<BR>\n" );
document.write( "By the looks of this equation I thought that the hyperbola was vertical.<BR>\n" );
document.write( "Then what I did was :  a= &#8730;2  b= 2   <BR>\n" );
document.write( "->  y= bx/a     and    y= -bx/a  so ->  y=2x&#8730;2/ 2  (Removed the root from the denominator) and  y=-2x&#8730;2/2\r<BR>\n" );
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document.write( "Now I had to find the foci:\r<BR>\n" );
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document.write( "c^2= a^2 + b^2   ->  c^2= 2+4= 6   -> c=&#8730;6   \r<BR>\n" );
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document.write( "Since the hyperbola is vertical this is how the foci should look like:  \r<BR>\n" );
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document.write( "(0,c) and (0, -c)  ->  (0, &#8730;6) and (0, -&#8730;6)\r<BR>\n" );
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document.write( "Is my solution correct?\r<BR>\n" );
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document.write( "Thank you for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537390 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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/cgi-bin/show-face.mpl?user=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=537390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hyperbola<BR>\n" );
document.write( "foci | ((0, -sqrt(6))  |  (0, sqrt(6)))=((0, -2.44949)  |  (0, 2.44949))<BR>\n" );
document.write( "vertices | (0, -2)  |  (0, 2)<BR>\n" );
document.write( "center | (0, 0)<BR>\n" );
document.write( "semimajor axis length | 2<BR>\n" );
document.write( "semiminor axis length | sqrt(2)=1.41421<BR>\n" );
document.write( "focal parameter | sqrt(2/3)=0.816497<BR>\n" );
document.write( "eccentricity | sqrt(3/2)=1.22474<BR>\n" );
document.write( "asymptotes | y = -sqrt(2) x  |  y = sqrt(2) x </SPAN>\n" );
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