document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130622>Question 1130622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of an ellipse that passes through A(3,5) and B(7,5/3) whose axis coincides with the coordinate axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747333 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747333\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "An ellipse has two axes; and there are two coordinate axes.  So when the statement of the problem sloppily says \"the\" axis of the ellipse coincides with \"the\" coordinate axis, I will assume that the intended meaning is that both axes of the ellipse coincide with both coordinate axes -- i.e., the center of the ellipse is at the origin.<br><BR>\n" );
document.write( "Then the equation of the ellipse is <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Form two equations in a^2 and b^2 using the two known points on the ellipse and solve the pair of equations to find the equation of the ellipse.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fa%5E2%2B25%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"9%2Fa%5E2%2B25%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2Fa%5E2%2B%2825%2F9%29%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"49%2Fa%5E2%2B%2825%2F9%29%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply the second equation by 9 and subtract one equation from the other to eliminate b:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=441%2Fa%5E2%2B25%2Fb%5E2+=+9 ALIGN=MIDDLE  ALT=\"441%2Fa%5E2%2B25%2Fb%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2Fa%5E2+=+8 ALIGN=MIDDLE  ALT=\"432%2Fa%5E2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a%5E2+=+432 ALIGN=MIDDLE  ALT=\"8a%5E2+=+432\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+54 ALIGN=MIDDLE  ALT=\"a%5E2+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute in either original equation to find b^2:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F54%2B25%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"9%2F54%2B25%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Fb%5E2+=+1-9%2F54+=+1-1%2F6+=+5%2F6 ALIGN=MIDDLE  ALT=\"25%2Fb%5E2+=+1-9%2F54+=+1-1%2F6+=+5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5b%5E2+=+150 ALIGN=MIDDLE  ALT=\"5b%5E2+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+30 ALIGN=MIDDLE  ALT=\"b%5E2+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We nowknow a^2 and b^2 for the ellipse, so we can write its equation:<br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F54%2By%5E2%2F30+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F54%2By%5E2%2F30+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );