document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88883>Question 88883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a problem with a graph. Here is the link. \r<BR>\n" );
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document.write( "http://s194.photobucket.com/albums/z4/dbrine/?action=view&current=t6q12.jpg </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64570 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=64570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First lets find the center:\r<BR>\n" );
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document.write( "Since the ellipse stretches from x=1 to x=9, this means the horizontal center is the average of 1 and 9. So add 1 and 9 and divide by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B9%29%2F2=10%2F2=5 ALIGN=MIDDLE  ALT=\"%281%2B9%29%2F2=10%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the horizontal center is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the ellipse stretches from y=1 to x=7, this means the vertical center is the average of 1 and 7. So add 1 and 7 and divide by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B7%29%2F2=8%2F2=4 ALIGN=MIDDLE  ALT=\"%281%2B7%29%2F2=8%2F2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the vertical center is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the center of the ellipse is (5,4)\r<BR>\n" );
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document.write( "Now lets find the radii:\r<BR>\n" );
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document.write( "Now we can find the horizontal radius by subtracting 5 from 9 (this will find the distance from the horizontal center to either the left or right edge)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-5=4 ALIGN=MIDDLE  ALT=\"9-5=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the horizontal radius is 4 (ie it is 4 units from the center to the edge if you use the x-axis)\r<BR>\n" );
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document.write( "We can find the vertical radius by subtracting 4 from 7 (this will find the distance from the vertical center to either the top or bottom edge)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-4=3 ALIGN=MIDDLE  ALT=\"7-4=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the vertical radius is 3 (ie it is 3 units from the center to the edge if you use the y-axis)\r<BR>\n" );
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document.write( "Now using the general equation of the ellipse \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%2B%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > where (h,k) is the center, a is the horizontal radius, and  b is the vertical radius\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2F4%5E2%2B%28y-4%29%5E2%2F3%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2F4%5E2%2B%28y-4%29%5E2%2F3%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=4 ALIGN=MIDDLE  ALT=\"k=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these were solved for earlier)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2F16%2B%28y-4%29%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2F16%2B%28y-4%29%5E2%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square each value\r<BR>\n" );
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document.write( "Notice if we graph the equation (you need to solve for y first) we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%0D%0Agrid%281%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%289%281-%28x-5%29%5E2%2F16%29%29%2B4%2C+-sqrt%289%281-%28x-5%29%5E2%2F16%29%29%2B4%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and this shows that our answer is correct.\r<BR>\n" );
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document.write( "So the answer is B) </SPAN>\n" );
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