document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389516>Question 389516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It asks for the standard form of the equation of this conic:\r<BR>\n" );
document.write( "\n" );
document.write( "4x^2 - 5y^2 - 16x - 30y - 9 = 0<BR>\n" );
document.write( "I know the standard form is going to be the form of a hyperbola, since a and c are not equal and have opposite signs.\r<BR>\n" );
document.write( "\n" );
document.write( "I also know that completing the square is part of solving this too, I just don't really know how to apply it to a conic. \r<BR>\n" );
document.write( "\n" );
document.write( "Help is much appreciated!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276036 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><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=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the properties of the Conic solution:\r<BR>\n" );
document.write( "\n" );
document.write( "4x^(2)-5y^(2)-16x-30y-9=0\r<BR>\n" );
document.write( "\n" );
document.write( "Move all terms not containing a variable to the right-hand side of the equation.<BR>\n" );
document.write( "4x^(2)-16x-5y^(2)-30y=9\r<BR>\n" );
document.write( "\n" );
document.write( "To create a trinomial square on the left-hand side of the equation, add a value to both sides of the equation that is equal to the square of half the coefficient of x.  In this problem, add (-2)^(2) to both sides of the equation.<BR>\n" );
document.write( "4(x^(2)-4x+4)-5y^(2)-30y=9+0+4*4\r<BR>\n" );
document.write( "\n" );
document.write( "Factor the perfect trinomial square into (x-2)^(2).<BR>\n" );
document.write( "4((x-2)^(2))-5y^(2)-30y=9+0+4*4\r<BR>\n" );
document.write( "\n" );
document.write( "Factor the perfect trinomial square into (x-2)^(2).<BR>\n" );
document.write( "4(x-2)^(2)-5y^(2)-30y=9+0+4*4\r<BR>\n" );
document.write( "\n" );
document.write( "To create a trinomial square on the left-hand side of the equation, add a value to both sides of the equation that is equal to the square of half the coefficient of y.  In this problem, add (3)^(2) to both sides of the equation.<BR>\n" );
document.write( "4(x-2)^(2)-5(y^(2)+6y+9)=9+0+4*4+0+9*-5\r<BR>\n" );
document.write( "\n" );
document.write( "Factor the perfect trinomial square into (y+3)^(2).<BR>\n" );
document.write( "4(x-2)^(2)-5((y+3)^(2))=9+0+4*4+0+9*-5\r<BR>\n" );
document.write( "\n" );
document.write( "Factor the perfect trinomial square into (y+3)^(2).<BR>\n" );
document.write( "4(x-2)^(2)-5(y+3)^(2)=9+0+4*4+0+9*-5\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply 4 by 4 to get 16.<BR>\n" );
document.write( "4(x-2)^(2)-5(y+3)^(2)=9+0+16+0+9*-5\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply 9 by -5 to get -45.<BR>\n" );
document.write( "4(x-2)^(2)-5(y+3)^(2)=9+0+16+0-45\r<BR>\n" );
document.write( "\n" );
document.write( "Add 0 to 9 to get 9.<BR>\n" );
document.write( "4(x-2)^(2)-5(y+3)^(2)=9+16+0-45\r<BR>\n" );
document.write( "\n" );
document.write( "Add 16 to 9 to get 25.<BR>\n" );
document.write( "4(x-2)^(2)-5(y+3)^(2)=25+0-45\r<BR>\n" );
document.write( "\n" );
document.write( "Add 0 to 25 to get 25.<BR>\n" );
document.write( "4(x-2)^(2)-5(y+3)^(2)=25-45\r<BR>\n" );
document.write( "\n" );
document.write( "Subtract 45 from 25 to get -20.<BR>\n" );
document.write( "4(x-2)^(2)-5(y+3)^(2)=-20\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply each term in the equation by -1.<BR>\n" );
document.write( "(4(x-2)^(2)-5(y+3)^(2))*-1=-20*-1\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply (4(x-2)^(2)-5(y+3)^(2)) by -1 to get -(4(x-2)^(2)-5(y+3)^(2)).<BR>\n" );
document.write( "-(4(x-2)^(2)-5(y+3)^(2))=-20*-1\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply -20 by -1 to get 20.<BR>\n" );
document.write( "-(4(x-2)^(2)-5(y+3)^(2))=20\r<BR>\n" );
document.write( "\n" );
document.write( "Divide each term by 20 to make the right-hand side equal to 1.<BR>\n" );
document.write( "-(4(x-2)^(2)-5(y+3)^(2))/(20)=(20)/(20)\r<BR>\n" );
document.write( "\n" );
document.write( "Simplify each term in the equation in order to set the right-hand side equal to 1.  The standard form of an ellipse or hyperbola requires the right-hand side of the equation be 1.<BR>\n" );
document.write( "-(4(x-2)^(2)-5(y+3)^(2))/(20)=1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let me know if this helps; if not, repost.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );