document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75566>Question 75566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me?  \r<BR>\n" );
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document.write( "1. Write the equation of an ellipse with center (8, 7), horizontal major axis length 16, and minor axis length 4.<BR>\n" );
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document.write( "2. Write the equation of an ellipse with center (9, –3), horizontal major axis length 18, and minor axis length 10.\r<BR>\n" );
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document.write( "Thankyou<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54224 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of the ellipse with center (h, k) is given by: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+h%29%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+k%29%5E2%2Fb%5E2 ALIGN=MIDDLE  ALT=\"%28y+-+k%29%5E2%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 \r<BR>\n" );
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document.write( "Where the length of the major axis is greater than the minor axis. \r<BR>\n" );
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document.write( "Here the centre is given by (8, 7)  and \r<BR>\n" );
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document.write( "length of the major axis = 2a =  16 \r<BR>\n" );
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document.write( "lenght of the minor axis = 2b = 4 \r<BR>\n" );
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document.write( "This implies that a = 8 and b = 2  \r<BR>\n" );
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document.write( "Hence, substituting these in the above formula, we have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+8%29%5E2%2F%288%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+8%29%5E2%2F%288%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+7%29%5E2%2F%282%29%5E2 ALIGN=MIDDLE  ALT=\"%28y+-+7%29%5E2%2F%282%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 \r<BR>\n" );
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document.write( "Simplifying these, we have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+8%29%5E2%2F64 ALIGN=MIDDLE  ALT=\"%28x+-+8%29%5E2%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+7%29%5E2%2F4 ALIGN=MIDDLE  ALT=\"%28y+-+7%29%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 \r<BR>\n" );
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document.write( "Taking LCM and simplifying this further, we have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+8%29%5E2+%2B+16%28y+-+7%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+8%29%5E2+%2B+16%28y+-+7%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 64 \r<BR>\n" );
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document.write( "Simplifying this again, we have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+16x+%2B+64+%2B+16%28y%5E2+%2B+49+-+14y%29 ALIGN=MIDDLE  ALT=\"x%5E2+-+16x+%2B+64+%2B+16%28y%5E2+%2B+49+-+14y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 64  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+16x+%2B+64+%2B+16y%5E2+%2B+784+-+224y ALIGN=MIDDLE  ALT=\"x%5E2+-+16x+%2B+64+%2B+16y%5E2+%2B+784+-+224y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 64 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+16y%5E2+-+16x+-+224y+%2B+848 ALIGN=MIDDLE  ALT=\"+x%5E2+-+16y%5E2+-+16x+-+224y+%2B+848\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 \r<BR>\n" );
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document.write( "This is the equation of the ellipse. \r<BR>\n" );
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document.write( "2. Write the equation of an ellipse with center (9, –3), horizontal major axis length 18, and minor axis length 10.\r<BR>\n" );
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document.write( "Solution:  \r<BR>\n" );
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document.write( "The equation of the ellipse with center (h, k) is given by: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+h%29%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+k%29%5E2%2Fb%5E2 ALIGN=MIDDLE  ALT=\"%28y+-+k%29%5E2%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 \r<BR>\n" );
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document.write( "Where the length of the major axis is greater than the minor axis. \r<BR>\n" );
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document.write( "Here the centre is given by (9, -3)  and \r<BR>\n" );
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document.write( "length of the major axis = 2a =  18 \r<BR>\n" );
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document.write( "length of the minor axis = 2b = 10 \r<BR>\n" );
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document.write( "This implies that a = 9 and b = 5  \r<BR>\n" );
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document.write( "Hence, substituting these in the above formula, we have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+9%29%5E2%2F%289%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+9%29%5E2%2F%289%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+%28-3%29%29%5E2%2F%285%29%5E2 ALIGN=MIDDLE  ALT=\"%28y+-+%28-3%29%29%5E2%2F%285%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+9%29%5E2%2F81 ALIGN=MIDDLE  ALT=\"%28x+-+9%29%5E2%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+%2B+3%29%5E2%2F25 ALIGN=MIDDLE  ALT=\"%28y+%2B+3%29%5E2%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 \r<BR>\n" );
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document.write( "Taking LCM, we get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28x+-+9%29%5E2+%2B+81%28y+%2B+3%29%5E2 ALIGN=MIDDLE  ALT=\"25%28x+-+9%29%5E2+%2B+81%28y+%2B+3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2025 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%28x%5E2+%2B+81+-+18y%29+%2B+81%28y%5E2+%2B+9+-+6y%29 ALIGN=MIDDLE  ALT=\"25%28x%5E2+%2B+81+-+18y%29+%2B+81%28y%5E2+%2B+9+-+6y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2025 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+%2B+2025+-+450x+%2B+81y%5E2+%2B+729+%2B+486y ALIGN=MIDDLE  ALT=\"25x%5E2+%2B+2025+-+450x+%2B+81y%5E2+%2B+729+%2B+486y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2025 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+%2B+2025+-+450x+%2B+81y%5E2+%2B+729+%2B+486y+-+2025 ALIGN=MIDDLE  ALT=\"25x%5E2+%2B+2025+-+450x+%2B+81y%5E2+%2B+729+%2B+486y+-+2025\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0 \r<BR>\n" );
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