document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006121>Question 1006121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with my homework on Analytic Geometry, please?\r<BR>\n" );
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document.write( "Here's the given problem:\r<BR>\n" );
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document.write( "Reduce this equation to standarm form 9x^2-4y^2+36x-16y-16=0. Find also the coordinates of the center, foci, and vertices. Draw also the asymptote and sketch the graph of the equation.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622270 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=622270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9x^2 -4y^2 +36x -16y -16 = 0<BR>\n" );
document.write( "this is the equation of a hyperbola<BR>\n" );
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document.write( "factor equation and complete the square<BR>\n" );
document.write( "9(x+2)^2 -4(y+2)^2 = 36<BR>\n" );
document.write( "now divide both sides of = by 36<BR>\n" );
document.write( "(x+2)^2 / 4 - (y+2) / 9 = 1<BR>\n" );
document.write( "this is standard form for hyperbola<BR>\n" );
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document.write( "center of hyperbola is (-2, -2)<BR>\n" );
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document.write( "vertices are (h+a,k) and (h-a,k), (0, -2) and (-4, -2)<BR>\n" );
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document.write( "to determine foci, first calculate c^2 = a^2 + b^2<BR>\n" );
document.write( "c^2 = 4 + 9<BR>\n" );
document.write( "c = sqrt(13)<BR>\n" );
document.write( "foci are (-2+sqrt(13), -2) and (-2-sqrt(13))<BR>\n" );
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document.write( "slope of asymptotes are + or - b/a = 9/4 and -9/4<BR>\n" );
document.write( "equations of asymptotes are y = k + or - b/a(x-h),<BR>\n" );
document.write( "y = -2 + (9/4)(x - 2) and y = -2 - (9/4)(x - 2)<BR>\n" );
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document.write( "here is the graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C+200%2C+-6%2C+2%2C+-6%2C+2%2C+%281%2F2%29%28-3sqrt%28x%5E2%2B4x%29-4%29%2C+%281%2F2%29%283sqrt%28x%5E2%2B4x%29-4%29%2C+-2%2B%289%2F4%29%28x%2B2%29%2C+-2-%289%2F4%29%28x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note that the left curve of the hyperbola is continuous, not sure why it is broken\r<BR>\n" );
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