document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204654>Question 1204654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the ellipse, determine the<BR>\n" );
document.write( "a)  coordinates of the center<BR>\n" );
document.write( "b) lengths of the major and minor axes<BR>\n" );
document.write( "c) coordinates of the foci\r<BR>\n" );
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document.write( "9x^2 + 25y^2  -  9x  -  50y  -  197.75 = 0\r<BR>\n" );
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document.write( "I did not get very far in this question. I was trying to first complete the square to factor into the standard form of the elliptical equation and move on from there.<BR>\n" );
document.write( "9x^2 + 25y^2  -  9x  -  50y  -  197.75 = 0<BR>\n" );
document.write( "9x^2  -  9x + 25y^2  -  50y = 197.75<BR>\n" );
document.write( "9(x^2  -  x) + 25(y^2  -  2y) = 197.75<BR>\n" );
document.write( "9(x^2  -  x + (1/4)) + 25(y^2  -  2y +1) = 197.75 + (1/4) + 1<BR>\n" );
document.write( "9(x  -  (1/2))^2 + 25(y - 1)^2 = 199<BR>\n" );
document.write( "I don’t know where to go from here because the numbers are troubling me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841062 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I appreciate that you've shown your work so far.<BR>\n" );
document.write( "You're on the right track. <BR>\n" );
document.write( "I'll start with the third step of your scratch work.\r<BR>\n" );
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document.write( "9(x^2 - x) + 25(y^2 - 2y) = 197.75<BR>\n" );
document.write( "9(x^2 - x + <font color=red>0</font>) + 25(y^2 - 2y + <font color=red>0</font>) = 197.75<BR>\n" );
document.write( "9(x^2 - x + <font color=red>0.25 - 0.25</font>) + 25(y^2 - 2y + <font color=red>1 - 1</font>) = 197.75<BR>\n" );
document.write( "9((x^2 - x + 0.25) - 0.25) + 25((y^2 - 2y + 1) - 1) = 197.75<BR>\n" );
document.write( "9((x-0.5)^2 - 0.25) + 25((y-1)^2 - 1) = 197.75<BR>\n" );
document.write( "9(x-0.5)^2 + 9(-0.25) + 25(y-1)^2 + 25(-1) = 197.75<BR>\n" );
document.write( "9(x-0.5)^2 - 2.25 + 25(y-1)^2 - 25 = 197.75<BR>\n" );
document.write( "9(x-0.5)^2 + 25(y-1)^2 - 27.25 = 197.75<BR>\n" );
document.write( "9(x-0.5)^2 + 25(y-1)^2 = 197.75 + 27.25<BR>\n" );
document.write( "9(x-0.5)^2 + 25(y-1)^2 = 225\r<BR>\n" );
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document.write( "I'll let you finish up. The goal is to get the ellipse equation into the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-h%29%5E2%29%2F%28a%5E2%29%2B%28%28y-k%29%5E2%29%2F%28b%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28%28x-h%29%5E2%29%2F%28a%5E2%29%2B%28%28y-k%29%5E2%29%2F%28b%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(h,k) = center of the ellipse<BR>\n" );
document.write( "a = half of the horizontal width<BR>\n" );
document.write( "b = half of the vertical height<BR>\n" );
document.write( "For example if a = 3 and b = 7 then the ellipse would be 2a = 2*3 = 6 units wide and 2b = 2*7 = 14 units tall.\r<BR>\n" );
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document.write( "In the steps where I've marked the terms in <font color=red>red</font>, I'm completing the square.<BR>\n" );
document.write( "For the (x^2-x) portion, the x coefficient is -1. That cuts in half to -0.5 and squares to 0.25<BR>\n" );
document.write( "We add and subtract 0.25 to help complete the square for the x terms.<BR>\n" );
document.write( "The y terms are the same idea: cut the y coefficient (-2) in half to get -1, then it squares to 1.\r<BR>\n" );
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document.write( "Use a graphing tool like GeoGebra or Desmos to check your answer.\r<BR>\n" );
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document.write( "If a > b, then the foci are located at (h-c, k) and (h+c, k) where,<BR>\n" );
document.write( "c^2 = a^2 - b^2<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "If b > a, then the foci are located at (h, k-c) and (h, k+c) where,<BR>\n" );
document.write( "c^2 = b^2 - a^2<BR>\n" );
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