document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180954>Question 1180954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hyperbola has vertices (1,9) and (13,9), and one of its foci is (−2,9). Find its standard equation. </SPAN>\n" );
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document.write( "The transverse axis (between the two vertices) is horizontal, so the branches of the hyperbola open left and right; the general equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The center is halfway between the two vertices, at (7,9).<br><BR>\n" );
document.write( "a is the distance from the center to either vertex, so a=6; a^2=36.<br><BR>\n" );
document.write( "c is the distance from the center to either focus, so c=9; c^2=81.<br><BR>\n" );
document.write( "b^2=c^2-a^2=45<br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%5E2%2F45-%28y-9%29%5E2%2F36=1 ALIGN=MIDDLE  ALT=\"%28x-7%29%5E2%2F45-%28y-9%29%5E2%2F36=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br> </SPAN>\n" );
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