document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1690>Question 1690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For each of the ff. quadratic equations, (a) identify the conic section represented (b) write the given equation in the standard form (c) give the properties (d) find the x and y-intercepts and (e) sketch the graph.\r<BR>\n" );
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document.write( "1.  2x^2-2y^2+20y-75=0<BR>\n" );
document.write( "2.  9x^2+4y^2-36x+8y+31=0\r<BR>\n" );
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document.write( "I need the answers now.  Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. 2x^2-2y^2+20y-75=0 <BR>\n" );
document.write( "   Sol: To complete the square : 2x^2-2(y^2-10y + (10/2)^2)=75-50 ,<BR>\n" );
document.write( "        So, 2x^2 - 2(y-5)^2 =25<BR>\n" );
document.write( "        Or x^2 - (y-5)^2 = 25/2    <BR>\n" );
document.write( "        Or x^2/(25/2) - (y-5)^2/(25/2) = 1<BR>\n" );
document.write( "        a) This is a hyperbola center at (0,5)<BR>\n" );
document.write( "        b) Standard form : x^2/(25/2) - (y-5)^2/(25/2) = 1<BR>\n" );
document.write( "        c) a hyperbola centered at (0,5), its axis is y=5.<BR>\n" );
document.write( "          (I am notsure what you mean about properties.)<BR>\n" );
document.write( "        d) when y =0 , x^2 = 25/2 + 25 = 75/2, so x= sqrt(75/2) or -sqrt(75/2)<BR>\n" );
document.write( "           (two x-intercepts).<BR>\n" );
document.write( "           when x = 0, -(y-5)^2 = 25/2 has no solutions ,so no y-intercepts.<BR>\n" );
document.write( "        e) Graph of the hyperbola is left for you.(It's easy.)\r<BR>\n" );
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document.write( "2. 9x^2+4y^2-36x+8y+31=0<BR>\n" );
document.write( "   Sol: By complete square : 9(x^2-4x+4) +4(y^2+2y +1) =-31+36+4 ,<BR>\n" );
document.write( "        Or 9(x-2)^2 + 4(y+1)^2 = 9,<BR>\n" );
document.write( "        Or (x-2)^2 + (y+1)^2/(9/4) = 1,<BR>\n" );
document.write( "        a) This is an ellipse centered at (2,-1)<BR>\n" );
document.write( "        b) Standard form : (x-2)^2 + (y+1)^2/(9/4) = 1,<BR>\n" );
document.write( "        c) an ellipse centered at (2,-1), its long axis a=3/2 is on y=-1,<BR>\n" );
document.write( "          short axis b is on x=2.<BR>\n" );
document.write( "          (I am notsure what you mean about properties.)<BR>\n" );
document.write( "        d)when y =0 , (x-2)^2 = 1-4/9 = 5/9, so x = 2 + sqrt(5)/3, or <BR>\n" );
document.write( "           x = 2-sqrt(5)/3. (two  x-intercepts)<BR>\n" );
document.write( "          when x =0, (y+1)^2 = 9/4(1-4). No solutions, so no y-intercepts.<BR>\n" );
document.write( "         e) Graph of the ellipse is left for you.\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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