document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=409759>Question 409759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi can you please help me with this question, graph the equation equal to:9x^2+16y^2+36x-32y-92=0  and find the vertix, focus point and axis of symmetry. Thank you all your help  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288632 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=288632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9x^2+16y^2+36x-32y-92=0<BR>\n" );
document.write( "find the vertex, focus point and axis of symmetry\r<BR>\n" );
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document.write( "9x^2+16y^2+36x-32y-92=0<BR>\n" );
document.write( "factor and completing the square (to complete the square, coefficients of x^2 and y^2 must be=1<BR>\n" );
document.write( "9(x^2+4x+4)+16(y^2-2y+1)=92+36+16=144<BR>\n" );
document.write( "9(x+2)^2+16(y-1)^2=144<BR>\n" );
document.write( "divide by 144<BR>\n" );
document.write( "(x+2)^2/16+(y-1)^2/9=1<BR>\n" );
document.write( "This is an ellipse with horizontal major axis and center at (-2,1)<BR>\n" );
document.write( "standard form of an ellipse: (x-h)^2/a^2+(y-k)^2/b^2=1<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=4<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "c^2=a^2-b^2=16-9=7<BR>\n" );
document.write( "c=sqrt(7)=2.65<BR>\n" );
document.write( "The vertices are on the horizontal major axis, at x=-2+-a=-2+-4=-6 and 2<BR>\n" );
document.write( "The focal points are also on the major axis, at x=-2+-c=-2+-sqrt(7)=-4.65 and .65. Axis of symmetry does not apply to ellipses<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "center:(-2,1)<BR>\n" );
document.write( "vertices:(-6,1),(2,1)<BR>\n" );
document.write( "foci:(-4.65,1),(.65,1)<BR>\n" );
document.write( "axis of symmetry does not apply to ellipse. It applies to parabolas.<BR>\n" );
document.write( "see the graph of the ellipse below:<BR>\n" );
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document.write( "y=1+((144-9(x+2)^2)/16)^.5\r<BR>\n" );
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