document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=607718>Question 607718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State whether the equation is a parobola, circle, or and elipse. Write the equation in the appropriate standard form and then give all the associated \"pieces.\"\r<BR>\n" );
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document.write( "5x^2+2y^2+30x-16y=-67\r<BR>\n" );
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document.write( "Thanks for any help you can give us!\r<BR>\n" );
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document.write( "michelle@modesto.net </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #382866 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=382866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x^2+2y^2+30x-16y=-67 \r<BR>\n" );
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document.write( "5x^2+30x+2y^2-16y=-67 \r<BR>\n" );
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document.write( "(5x^2+30x)+(2y^2-16y)=-67 \r<BR>\n" );
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document.write( "5(x^2+6x)+2(y^2-8y)=-67 \r<BR>\n" );
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document.write( "5(x^2+6x+9-9)+2(y^2-8y+16-16)=-67 \r<BR>\n" );
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document.write( "5((x^2+6x+9)-9)+2((y^2-8y+16)-16)=-67 \r<BR>\n" );
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document.write( "5((x+3)^2-9)+2((y-4)^2-16)=-67 \r<BR>\n" );
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document.write( "5(x+3)^2-5(9)+2(y-4)^2-2(16)=-67 \r<BR>\n" );
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document.write( "5(x+3)^2-45+2(y-4)^2-32=-67 \r<BR>\n" );
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document.write( "5(x+3)^2+2(y-4)^2-77=-67 \r<BR>\n" );
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document.write( "5(x+3)^2+2(y-4)^2=-67+77 \r<BR>\n" );
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document.write( "5(x+3)^2+2(y-4)^2=10\r<BR>\n" );
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document.write( "(5(x+3)^2)/10+(2(y-4)^2)/10=10/10\r<BR>\n" );
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document.write( "( (x+3)^2 )/2+( (y-4)^2 )/5 = 1\r<BR>\n" );
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document.write( "So this is an ellipse that is centered at (-3,4). <BR>\n" );
document.write( "It has a major axis that has a length of 2*sqrt(5) units and minor axis that has a length of 2*sqrt(2) units.\r<BR>\n" );
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document.write( "Note: the general form of an ellipse is ( (x-h)^2 )/(a^2)+( (y-k)^2 )/(b^2)=1\r<BR>\n" );
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document.write( "The center of this general ellipse is (h,k).<BR>\n" );
document.write( "The length of the major axis of this general ellipse is 2a (where a > b)<BR>\n" );
document.write( "The length of the minor axis of this general ellipse is 2b (where a > b)<BR>\n" );
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