document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189325>Question 1189325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A conic has an equation of an asymptote equal to 3x=4y. What is the equation of the conic having its center at <BR>\n" );
document.write( "origin and its transverse axis equal to y=0.<BR>\n" );
document.write( "a. 9x2-16y2 = 144 <BR>\n" );
document.write( "b. 16x2  -  9y2 = 144 <BR>\n" );
document.write( "c. 9y2  -  16x2 = 144 <BR>\n" );
document.write( "d. 16y2  -  9x2 = 144 </SPAN>\n" );
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document.write( "The transverse axis (connecting the two vertices of the hyperbola) is the line y=0, which is the x-axis, so the branches of the hyperbola open right and left.  So the equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So we can eliminate choices c and d.<br><BR>\n" );
document.write( "The slopes of the asymptotes are b/a and -b/a.  Given that one of the asymptotes has the equation 3x=4y, we have y=(3/4)x; therefore, b/a=3/4.  Then the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4%5E2-y%5E2%2F3%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4%5E2-y%5E2%2F3%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F16-y%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F16-y%5E2%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-16y%5E2=144 ALIGN=MIDDLE  ALT=\"9x%5E2-16y%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER a<br><BR>\n" );
document.write( " </SPAN>\n" );
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