document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975428>Question 975428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the ellipse:   9x2 + 4y2 + 18x - 48y + 117 = 0            \r<BR>\n" );
document.write( "\n" );
document.write( "     a) Put the equation in standard form             <BR>\n" );
document.write( "     <BR>\n" );
document.write( "     b) Horizontal or vertical major axis?            <BR>\n" );
document.write( "    <BR>\n" );
document.write( "     c) Find  center,  vertices, foci, <BR>\n" );
document.write( "         length of major and minor axes, <BR>\n" );
document.write( "        and eccentricity \r<BR>\n" );
document.write( "\n" );
document.write( "d)	Sketch a graph of this ellipse.                     <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597257 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=597257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ven the ellipse: 9x2 + 4y2 + 18x - 48y + 117 = 0 <BR>\n" );
document.write( "a) Put the equation in standard form <BR>\n" );
document.write( "b) Horizontal or vertical major axis? <BR>\n" );
document.write( "c) Find center, vertices, foci, <BR>\n" );
document.write( "length of major and minor axes, <BR>\n" );
document.write( "and eccentricity <BR>\n" );
document.write( "d)	Sketch a graph of this ellipse.<BR>\n" );
document.write( "***<BR>\n" );
document.write( "9x^2+18x+4y^2-48y=-117<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "9(x^2+2x+1)+4(y^2-12y+36)=-117+9+144<BR>\n" );
document.write( "9(x+1)^2+4(y-6)^2=36<BR>\n" );
document.write( "a)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E2%2F4%2B%28y-6%29%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E2%2F4%2B%28y-6%29%5E2%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b)this is an equation of an ellipse with vertical major axis<BR>\n" );
document.write( "its standard form of equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=coordinates of c)center<BR>\n" );
document.write( "center: (-1, 6)<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "length of major axis=2a=6<BR>\n" );
document.write( "vertices: (-1, 6±a)=(-1, 6±3)=(-1, 3) and (-1, 9)<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "length of minor axis=2b=4<BR>\n" );
document.write( "c^2=a^2-b^2=9-4=5<BR>\n" );
document.write( "c=&#8730;5&#8776;2.2<BR>\n" );
document.write( "foci:  (-1, 6±c)=(-1, 6±2.2)=(-1, 3.8) and (-1, 8.2)<BR>\n" );
document.write( "d)see graph below:<BR>\n" );
document.write( "y=((36-9(x+1)^2)/4)^.5+6<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%28%2836-9%28x%2B1%29%5E2%29%2F4%29%5E.5%2B6%2C-%28%2836-9%28x%2B1%29%5E2%29%2F4%29%5E.5%2B6%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );