document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=467310>Question 467310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please tell me which conic each of the following equations are? Thank you in advance!!! <BR>\n" );
document.write( "a. 12x^2 = 29y^2 - y + 39<BR>\n" );
document.write( "b. 12x^2 - 29y = x + 39<BR>\n" );
document.write( "c. 29y^2 + 12x^2 = x +39<BR>\n" );
document.write( "d. 12y^2 + 29y = 39 - 12x^2\r<BR>\n" );
document.write( "\n" );
document.write( "I posted this question earlier, but someone answered with no answer so I'm reposting. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320641 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=320641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can someone please tell me which conic each of the following equations are? Thank you in advance!!! <BR>\n" );
document.write( "a. 12x^2 = 29y^2 - y + 39<BR>\n" );
document.write( "b. 12x^2 - 29y = x + 39<BR>\n" );
document.write( "c. 29y^2 + 12x^2 = x +39<BR>\n" );
document.write( "d. 12y^2 + 29y = 39 - 12x^2<BR>\n" );
document.write( "...<BR>\n" );
document.write( "To determine which conic the equations above represent, the best way is to complete the square first.<BR>\n" );
document.write( "a. 12x^2 = 29y^2 - y + 39<BR>\n" );
document.write( "12x^2-29y^2+ y=39<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "12x^2-29(y^2-y/29+(1/58)^2)=39+29*(1/58)^2<BR>\n" );
document.write( "12x^2-29(y-(1/58)^2=39+29*(1/58)^2<BR>\n" );
document.write( "This is a hyperbola with a horizontal transverse axis with center at (0,1/58) (note the negative sign between the x and y terms and that the x-term comes first; if y-term comes first, then transverse axis is vertical)<BR>\n" );
document.write( "Standard form for hyperbola: (x-h)^2/a^2-(y-k)^2/b^2=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b. 12x^2 - 29y = x + 39<BR>\n" );
document.write( "29y=12x^2-x-39<BR>\n" );
document.write( "divide by 29<BR>\n" );
document.write( "y=(12/29)x^2-x/29-39/29<BR>\n" );
document.write( "=12/29(x^2-x/12+(1/24)^2)-39/29-(1/24)^2<BR>\n" );
document.write( "=12/29(x-1/24)^2)-(39/29+(1/24)^2)<BR>\n" );
document.write( "This is a parabola which opens upwards with vertex at (1/24,-(39/29+(1/24)^2)) <BR>\n" );
document.write( "Standard form a parabola: y=A(x-h)^2+k<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c. 29y^2 + 12x^2 = x +39<BR>\n" );
document.write( " 29y^2+12x^2-x =39<BR>\n" );
document.write( "29y^2+12(x^2-x/12+(1/24)^2) =39+12*(1/24)^2<BR>\n" );
document.write( "29y^2+12(x-(1/24)^2=39+12*(1/24)^2<BR>\n" );
document.write( "This is an ellipse with a vertical major axis and center at (1/24,0),(note how this differs from the equation of a hyperbola in that there is a plus sign between the x and y terms. If (x-h)^2 has the larger denominator, major axis is horizontal. Conversely, if (y-k)^2 has the larger denominator, major axis is vertical.<BR>\n" );
document.write( "Standard form of ellipse: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "d. 12y^2 + 29y = 39 - 12x^2<BR>\n" );
document.write( "12y^2+29y+12x^2=39<BR>\n" );
document.write( "12(y^2+29y/12+(29/24)^2)+12x^2=39+12*(29/24)^2<BR>\n" );
document.write( "12(y+29/24)^2+12x^2=39+12*(29/24)^2<BR>\n" );
document.write( "divide by 12<BR>\n" );
document.write( "(y+29/24)^2+x^2=[39+12*(29/24)^2]/12<BR>\n" );
document.write( "This is a circle with center at (0,-29/24) and a radius=sqrt([39+12*(29/24)^2]/12)<BR>\n" );
document.write( "standard form for circle (x-h)^2+(y-k)^2=r^2<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );