document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74290>Question 74290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the center, vertices and foci of the following ellipse:\r<BR>\n" );
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document.write( "(x + 3)^2/9 + (y + 1)^2/16 =1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53304 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=53304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the center, vertices and foci of the following ellipse:\r<BR>\n" );
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document.write( "(x + 3)^2/9 + (y + 1)^2/16 =1<BR>\n" );
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document.write( "The equation for an ellipse whose denominator is largest under the y's is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Characteristics:<BR>\n" );
document.write( "a>b and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=a%5E2-c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=a%5E2-c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Major axis is parallel to the y-axis.<BR>\n" );
document.write( "Center:(h,k)<BR>\n" );
document.write( "Foci: (h,k+c), (h,k-c)<BR>\n" );
document.write( "Vertices: (h,k+a), (h,k-a)<BR>\n" );
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document.write( "Your equation has:<BR>\n" );
document.write( "h=-3<BR>\n" );
document.write( "k=-1<BR>\n" );
document.write( "a^2=16--->a=4<BR>\n" );
document.write( "b^2=9---->b=3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=a%5E2-c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2=a%5E2-c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-a%5E2=-c%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-a%5E2=-c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%5E2%2Ba%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"-b%5E2%2Ba%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2B16=c%5E2 ALIGN=MIDDLE  ALT=\"-9%2B16=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=c%5E2 ALIGN=MIDDLE  ALT=\"7=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29=c ALIGN=MIDDLE  ALT=\"sqrt%287%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore, the center: (h,k)=(-3,-1) <BR>\n" );
document.write( "Foci: (h,k+c), (h,k-c)=(-3,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Bsqrt%287%29 ALIGN=MIDDLE  ALT=\"-1%2Bsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (-3,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1-sqrt%287%29 ALIGN=MIDDLE  ALT=\"-1-sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Vertices: (h,k+a), (h,k-a)=(-3,-1+4),(-3,-1-4)==>(-3,3),(-3,-5)<BR>\n" );
document.write( "Happy Calculating!!!! </SPAN>\n" );
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