document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=928503>Question 928503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ) Use the discriminant to determine whether the graph of the<BR>\n" );
document.write( "equation 13x^2+6 square root 3+7y^2 +16 is a parabola, an ellipse, or a hyperbola.<BR>\n" );
document.write( "Use a rotation of axes to eliminate the xy-term and sketch the graph. \r<BR>\n" );
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document.write( "I got that the equation was going to be an ellipse <BR>\n" );
document.write( "i got that x= 1square root3/ 2 X- 1/2Y<BR>\n" );
document.write( "y=1/2X+square root3/2Y\r<BR>\n" );
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document.write( "but when i plug them into the original equation the xy term does not cancel out I dont know what i did wrong </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563659 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=563659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 13x^2+6 square root 3+7y^2 +16 <BR>\n" );
document.write( "this is an ellipic paraboloid <BR>\n" );
document.write( "polynomial discriminant is<BR>\n" );
document.write( "delta x = -52(7y^2 +(6*square root(3)) +16)<BR>\n" );
document.write( "min is (16 + (6*square root(3))) at (x,y) = (0,0)<BR>\n" );
document.write( "y = square root(-13x^2 -(6*square root(3)) -16) / square root(7)<BR>\n" );
document.write( "y = -square root(-13x^2 -(6*square root(3)) -16) / square root(7)<BR>\n" );
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