document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449299>Question 449299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We are working on conic sections. I need help finding the equation of an ellipse with these given points: vartices at (-1,2) and (7,2)and a focus at (5,2). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309103 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=309103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are working on conic sections. I need help finding the equation of an ellipse with these given points: vartices at (-1,2) and (7,2)and a focus at (5,2).<BR>\n" );
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document.write( "Standard form for an ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b),<BR>\n" );
document.write( "with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form for an 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. Note that the only difference between these two forms is that the a^2 and b^2 terms are interchanged.<BR>\n" );
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document.write( "For given ellipse:<BR>\n" );
document.write( "Since the vertices are horizontal, this ellipse is of the first form listed above.\r<BR>\n" );
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document.write( "x-coordinate of center =(-1+7)/2=3<BR>\n" );
document.write( "y-coordinate of center=2<BR>\n" );
document.write( "Center is at (3,2) <BR>\n" );
document.write( "Length of major axis=distance between end points of vertices=8=2a<BR>\n" );
document.write( "a=4<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "c=distance from center to focal point on major axis=5-3=2<BR>\n" );
document.write( "c^2=4<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=16-4=12<BR>\n" );
document.write( "b=&#8730;12<BR>\n" );
document.write( "you now have all the information you need to write the equation of given ellipse as follows:\r<BR>\n" );
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document.write( "(x-3)^2/16+(y-2)^2/12=1<BR>\n" );
document.write( "See the graph below as visual evidence of this equation\r<BR>\n" );
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document.write( "...<BR>\n" );
document.write( "y=(12(1-(x-3)^2/16))^.5+2\r<BR>\n" );
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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%2812%281-%28x-3%29%5E2%2F16%29%29%5E.5%2B2%2C-%2812%281-%28x-3%29%5E2%2F16%29%29%5E.5%2B2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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