document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=456707>Question 456707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for an ellipse with center (1,-3), vertices (1,2) and (1,-8), and co-vertices (4,-3) and (-2,-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313743 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=313743\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation for an ellipse with center (1,-3), vertices (1,2) and (1,-8), and co-vertices (4,-3) and (-2,-3).<BR>\n" );
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document.write( "Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between the two forms is the interchange of a^2 and b^2.<BR>\n" );
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document.write( "Given center at (1,-3)<BR>\n" );
document.write( "Since the x-coordinates of the end points of the vertices are the same at 1, given ellipse has a vertical major axis on x=1.<BR>\n" );
document.write( "length of major axis=10=2a<BR>\n" );
document.write( "a=5<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "co-vertices or minor axis on y=-3<BR>\n" );
document.write( "length of minor axis=6=2b<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "b^2=9<BR>\n" );
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document.write( "Equation: (x-1)^2/9+(y+3)^2/25=1 (ans)<BR>\n" );
document.write( "see graph below as a visual check on the algebra above. Note the center and length and end points of major and minor axes.<BR>\n" );
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document.write( "y=(25-25(x-1)^2/9)^.5-3<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+%2825-25%28x-1%29%5E2%2F9%29%5E.5-3%2C-%2825-25%28x-1%29%5E2%2F9%29%5E.5-3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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