document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=434883>Question 434883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the foci for each hyperbola and sketch a graph\r<BR>\n" );
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document.write( "Y^2/49-x^2/16=1 <BR>\n" );
document.write( "5x^2-10y^2=80 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302182 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=302182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the foci for each hyperbola and sketch a graph <BR>\n" );
document.write( "Y^2/49-x^2/16=1 <BR>\n" );
document.write( "5x^2-10y^2=80<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of 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( "Standard form of hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) again being the (x,y) coordinates of the center.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Y^2/49-x^2/16=1<BR>\n" );
document.write( "This is a hyperbola with center at (0,0) and with a vertical transverse axis.<BR>\n" );
document.write( "a^2=49<BR>\n" );
document.write( "a=7 (distance from center to vertices)<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "c^2=a^2+b^2=49+16=65<BR>\n" );
document.write( "c=sqrt(65)=8.06..(distance from center to foci)<BR>\n" );
document.write( "Equation of asymptotes:y=+-(a/b)x=+-(7/4)x<BR>\n" );
document.write( "see the graph of the hyperbola below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=+-(49((x^2/16)+1))^.5<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+%2849%28%28x%5E2%2F16%29%2B1%29%29%5E.5%2C-%2849%28%28x%5E2%2F16%29%2B1%29%29%5E.5%2C7x%2F4%2C-7x%2F4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "5x^2-10y^2=80<BR>\n" );
document.write( "x^2/16-y^2/8=1<BR>\n" );
document.write( "This is a hyperbola with center at (0,0) but with a horizontal transverse axis.<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=4 (distance from center to vertices)<BR>\n" );
document.write( "b^2=8<BR>\n" );
document.write( "b=sqrt(8)=2.83<BR>\n" );
document.write( "c^2=a^2+b^2=16+8=24<BR>\n" );
document.write( "c=sqrt(24)=4.9(distance from center to foci)<BR>\n" );
document.write( "Equation of asymptotes:y=+-(b/a)x=+-(2.83/4)x<BR>\n" );
document.write( "see the graph of the hyperbola below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=+-(x^2/2-8)^.5\r<BR>\n" );
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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+%28x%5E2%2F2-8%29%5E.5%2C-%28x%5E2%2F2-8%29%5E.5%2C%282.83%2F4%29x%2C-%282.83%2F4%29x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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