document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=688516>Question 688516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the equation of the ellipse, find the coordinates of the CENTER, FOCI, and VERTICES. THEN GRAPH. <BR>\n" );
document.write( "4x^2+9y^2-8x+36y+4=0\r<BR>\n" );
document.write( "\n" );
document.write( "Please help I've been doing this homework for an hour.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425673 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=425673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the equation of the ellipse, find the coordinates of the CENTER, FOCI, and VERTICES. THEN GRAPH. <BR>\n" );
document.write( "4x^2+9y^2-8x+36y+4=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "4x^2-8x+9y^2+36y+4=0<BR>\n" );
document.write( "4(x^2-2x+1)+9(y^2+4y+4)=-4+4+36<BR>\n" );
document.write( "4(x-1)^2+9(y+2)^2=36<BR>\n" );
document.write( "(x-1)^2/9+(y+2)^2/4=1<BR>\n" );
document.write( "This is an equation of an ellipse with horizontal major axis.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "For given ellipse:<BR>\n" );
document.write( "center:(1,-2)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=&#8730;9=3<BR>\n" );
document.write( "vertices: (1±a,-2)=(1±3,-2)=(4,-2) and (-2,-2)<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "b=&#8730;4=2<BR>\n" );
document.write( "c^2=a^2-b^2=9-4=5<BR>\n" );
document.write( "c=&#8730;5&#8776;2.24<BR>\n" );
document.write( "Foci:(1±c,-2)=(1±2.24,-2)=(3.24,-2) and (-1.24,-2)<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=±(4-(4(x-1)^2/9))^.5-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%284-%284%28x-1%29%5E2%2F9%29%29%5E.5-2%2C-%284-%284%28x-1%29%5E2%2F9%29%29%5E.5-2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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