document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106320>Question 1106320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I write -4x^2 + 9y^2 + 32x + 36y - 64 = 0 in standard form? What are the steps? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721291 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) complete the squares in both x and y; and<BR>\n" );
document.write( "(2) divide by the appropriate constant to get \"1\" on the right hand side.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2+%2B+9y%5E2+%2B+32x+%2B+36y+-+64+=+0 ALIGN=MIDDLE  ALT=\"-4x%5E2+%2B+9y%5E2+%2B+32x+%2B+36y+-+64+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [original equation]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B32x%2B9y%5E2%2B36y+=+64 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B32x%2B9y%5E2%2B36y+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [group the x terms and y terms; move constant to other side]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x%5E2-8x%29%2B9%28y%5E2%2B4y%29+=+64 ALIGN=MIDDLE  ALT=\"-4%28x%5E2-8x%29%2B9%28y%5E2%2B4y%29+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [factor out the leading coefficients for both x and y]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x%5E2-8x%2B16%29%2B9%28y%5E2%2B4y%2B4%29+=+64-4%2816%29%2B9%284%29+=+36 ALIGN=MIDDLE  ALT=\"-4%28x%5E2-8x%2B16%29%2B9%28y%5E2%2B4y%2B4%29+=+64-4%2816%29%2B9%284%29+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [complete the squares in x and y, adding the same quantities to both sides of the equation]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2F36%29%28x-4%29%5E2%2B%289%2F36%29%28y%2B2%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28-4%2F36%29%28x-4%29%5E2%2B%289%2F36%29%28y%2B2%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [divide by the constant on the right to make the right side \"1\"]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-4%29%5E2%2F9%2B%28y%2B2%29%5E2%2F4+=+1 ALIGN=MIDDLE  ALT=\"-%28x-4%29%5E2%2F9%2B%28y%2B2%29%5E2%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [simplify and re-format]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B2%29%5E2%2F4-%28x-4%29%5E2%2F9+=+1 ALIGN=MIDDLE  ALT=\"%28y%2B2%29%5E2%2F4-%28x-4%29%5E2%2F9+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [rearrange terms to get positive term first on left hand side]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B2%29%5E2%2F2%5E2-%28x-4%29%5E2%2F3%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28y%2B2%29%5E2%2F2%5E2-%28x-4%29%5E2%2F3%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [write in final standard form]<br><BR>\n" );
document.write( "The equation is of a hyperbola with center (4,-2); asymptotes with slopes 2/3 and -2/3; branches opening upward and downward.<br><BR>\n" );
document.write( "A graph: 2 branches of the hyperbola (red, green); asymptotes (blue, purple).  The center is at the intersection of the asymptotes.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-8%2C16%2C-10%2C10%2Csqrt%284%2B%284%28x-4%29%5E2%2F9%29%29-2%2C-sqrt%284%2B%284%28x-4%29%5E2%2F9%29%29-2%2C%282%2F3%29%28x-4%29-2%2C%28-2%2F3%29%28x-4%29-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );