document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969561>Question 969561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the conic: 9x^2 + 2y^2 + 100y - 72x + 19 = 0, give its properties and sketch the graph </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592990 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=592990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the conic: 9x^2 + 2y^2 + 100y - 72x + 19 = 0, give its properties and sketch the graph.<BR>\n" );
document.write( "***<BR>\n" );
document.write( "9x^2- 72x + 2y^2 + 100y  + 19 = 0<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "9(x^2-8x+16) + 2(y^2+50y+625) =-19+144+1350<BR>\n" );
document.write( "9(x-4)^2+2(y+25)^2=1475<BR>\n" );
document.write( "equation of given ellipse:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2F%281475%2F9%29%2B%28y%2B25%29%5E2%2F%281475%2F2%29=1 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2F%281475%2F9%29%2B%28y%2B25%29%5E2%2F%281475%2F2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of an ellipse with vertical major axis.<BR>\n" );
document.write( "Ita standard form of equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=coordinates of center.<BR>\n" );
document.write( "For given ellipse:<BR>\n" );
document.write( "center: (4, -25)<BR>\n" );
document.write( "a^2=1475/2<BR>\n" );
document.write( "a=&#8730;(1475/2)&#8776;27.2 (distance from center to vertices)<BR>\n" );
document.write( "b^2=1475/9<BR>\n" );
document.write( "b=&#8730;(1479/9)&#8776;12.8 (distance from center to co-vertices)<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-80%2C80%2C+-80%2C80%2C%28737.5-%28737.5%2A%28x-4%29%5E2%2F163.9%29%29%5E.5-25%2C-%28737.5-%28737.5%2A%28x-4%29%5E2%2F163.9%29%29%5E.5-25%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );