document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39221>Question 39221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the conic section represented by the equation by writing the equation in standard form. For a parabola, give the vertex. For a circle, give the center and the radius. For an ellipse or hyperbola, give the center and the foci. Sketch the graph.<BR>\n" );
document.write( "16x^2+96x-9y^2+36y=36 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24855 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING EXAMPLES AND TRY .IF STILL IN DIFFICULTY PLEASE COME BACK<BR>\n" );
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document.write( "I was wondering if anyone could help me determine what<BR>\n" );
document.write( "type of figure is given, then graph. Show all work and<BR>\n" );
document.write( "label all key points (asymptotes, foci, vertices, the<BR>\n" );
document.write( "directrix, the center) where applicable.<BR>\n" );
document.write( "x^2 – 4x – 8y = 12<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 22495 by venugopalramana(1898) About Me  on<BR>\n" );
document.write( "2006-05-07 08:31:50 (Show Source):<BR>\n" );
document.write( "TIP:<BR>\n" );
document.write( "2.IF X^2 OR Y^2 IS ONLY PRESENT ,IT COULD BE A<BR>\n" );
document.write( "PARABOLA.<BR>\n" );
document.write( "2.) x2 – 4x – 8y = 12<BR>\n" );
document.write( "COMPLETE SQUARE<BR>\n" );
document.write( "(X^2-2*2X+2^2)-2^2=12+8Y<BR>\n" );
document.write( "(X-2)^2=8Y+16=8(Y+2)<BR>\n" );
document.write( "THIS IS THE EQN.OF A PARABOLA .STD EQN. IS<BR>\n" );
document.write( "(X-H)^2=4A(Y-K),WHERE<BR>\n" );
document.write( "(H,K) IS THE VERTEX....(2,-2) HERE.<BR>\n" );
document.write( "4A=LATUS RECTUM =8 HERE...A=2<BR>\n" );
document.write( "FOCUS IS (H+A,K).....(2+2,-2)=(4,-2)..HERE.<BR>\n" );
document.write( "DIRECTRIX IS X-H+A=0...<BR>\n" );
document.write( "X-2+2=0...OR....X=0..<BR>\n" );
document.write( "AXIS IS Y-K =0..Y+2=0<BR>\n" );
document.write( "graph( 500, 500, -20, 20, -20, 20,(x^2-4*x-12)/8 )\r<BR>\n" );
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document.write( "Quadratic-relations-and-conic-sections/36550: I was<BR>\n" );
document.write( "wondering if anyone could help me determine what type<BR>\n" );
document.write( "of figure is given, then graph. Show all work and<BR>\n" );
document.write( "label all key points (asymptotes, foci, vertices, the<BR>\n" );
document.write( "directrix, the center) where applicable.<BR>\n" );
document.write( "9x^2 – 96y = 16y^2 + 18x + 279<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 22493 by venugopalramana(1898) About Me  on<BR>\n" );
document.write( "2006-05-07 08:27:57 (Show Source):<BR>\n" );
document.write( "TIP<BR>\n" );
document.write( "IF X^2 AND Y^2 HAVE DIFFERENT COEFFICIENTS WITH<BR>\n" );
document.write( "OPPOSITE SIGNS THEN IT<BR>\n" );
document.write( "COULD BE HYPERBOLA<BR>\n" );
document.write( "3.) 9x2 – 96y = 16y2 + 18x + 279<BR>\n" );
document.write( "COMPLETE SQUARE...<BR>\n" );
document.write( "{(3X)^2-2*3X*3+3^2}-3^2-{(4Y)^2+2*4Y*12+12^2}-12^2=279<BR>\n" );
document.write( "(3X+3)^2-(4Y+12)^2=279+9+144=432<BR>\n" );
document.write( "9(X+1)^2-16(Y+3)^2=432......NOW DIVIDE THROUGH OUT<BR>\n" );
document.write( "WITH 432 TO GET 1 ON THE RHS.<BR>\n" );
document.write( "(X+1)^2/(432/9) -(Y+3)^2/(432/16)=1<BR>\n" );
document.write( "(X+1)^2/48 - (Y+3)^2/27 =1<BR>\n" );
document.write( "THIS THE EQN. OF A HYPERBOLA.STD.EQN.IS.<BR>\n" );
document.write( "(X-H)^2/A^2 - (Y-K)^2/B^2=1..WHERE<BR>\n" );
document.write( "(H,K) IS CENTRE.....(-1,-3) HERE<BR>\n" );
document.write( "TRANSVERSE AXIS IS Y=K...Y=-3<BR>\n" );
document.write( "LENGTH OF TRANSVERSE AXIS=2A..<BR>\n" );
document.write( "...=2SQRT(48)<BR>\n" );
document.write( "CONJUGATE AXIS IS X=H.......X=-1<BR>\n" );
document.write( "LENGTH OF CONJUGATE AXIS = 2B<BR>\n" );
document.write( "=2SQRT(27)<BR>\n" );
document.write( "ECCENTRICITY=E=SQRT{(A^2+B^2)/A^2}<BR>\n" );
document.write( "=SQRT{(48+27)/48}=SQRT(75/48)<BR>\n" );
document.write( "A*E=SQRT(48)*SQRT(75/48)=SQRT(75)<BR>\n" );
document.write( "FOCI ARE (H+-AE,K)......(-1+SQRT(75),-3)<BR>\n" );
document.write( "AND ......(-1-SQRT(75),-3)<BR>\n" );
document.write( "A/E=SQRT(48)/SQRT(75/48)=48/SQRT(75)<BR>\n" );
document.write( "DIRECTRIX ARE X=H+-A/E....<BR>\n" );
document.write( "X=-1+48/SQRT(75)...AND<BR>\n" );
document.write( "X=-1-48/SQRT(75)<BR>\n" );
document.write( "ASYMPTOTES ARE GIVEN BY<BR>\n" );
document.write( "(X-H)^2/A^2 = (Y-K)^2/B^2<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "(X-H)/A=+(Y-K)/B AND............(X+1)/SQRT(48)<BR>\n" );
document.write( "=(Y+3)/SQRT(27)<BR>\n" );
document.write( "(X-H)/A=-(Y-K)/B.............(X+1)/SQRT(48) =<BR>\n" );
document.write( "-(Y+3)/SQRT(27)<BR>\n" );
document.write( "GRAPH IS GIVEN BELOW..<BR>\n" );
document.write( "graph( 500, 500, -50, 50, -50, 50,<BR>\n" );
document.write( "-3+27*(((x+1)^2-48)/48)^0.5,-3-27*(((x+1)^2-48)/48)^0.5)<BR>\n" );
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document.write( "\n" );
document.write( "Quadratic-relations-and-conic-sections/36551: I was<BR>\n" );
document.write( "wondering if anyone could help me determine what type<BR>\n" );
document.write( "of figure is given, then graph. Show all work and<BR>\n" );
document.write( "label all key points (asymptotes, foci, vertices, the<BR>\n" );
document.write( "directrix, the center) where applicable.<BR>\n" );
document.write( "4(x-1)2 = 4-y^2<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 22486 by venugopalramana(1898) About Me  on<BR>\n" );
document.write( "2006-05-07 06:33:13 (Show Source):<BR>\n" );
document.write( "TIP:<BR>\n" );
document.write( "IF X^2 AND Y^2 HAVE DIFFERENT COEFFICIENTS OF SAME<BR>\n" );
document.write( "SIGN ,THEN IT COULD<BR>\n" );
document.write( "BE ELLIPSE.<BR>\n" );
document.write( "4.) 4(x-1)2 = 4-y2<BR>\n" );
document.write( "I HOPE IT IS<BR>\n" );
document.write( "4(X-1)^2+Y^2=4...DIVIDE WITH 4<BR>\n" );
document.write( "(X-1)^2/1^2+Y^2/2^2=1<BR>\n" );
document.write( "THIS THE EQN.OF AN ELLIPSE.STD.EQN. IS<BR>\n" );
document.write( "(X-H)^2/A^2 +(Y-K)^2/B^2=1<BR>\n" );
document.write( "WHERE<BR>\n" );
document.write( "(H,K) IS CENTRTE....(1,0).HERE<BR>\n" );
document.write( "LENGTH OF MAJOR AXIS IS 2B...2*2=4<BR>\n" );
document.write( "MINOR AXIS IS ALONG Y=K....Y=0<BR>\n" );
document.write( "LENGTH OF MINOR AXIS IS 2A...2*1=2<BR>\n" );
document.write( "ECCENTRICITY=E=SQRT{(B^2-A^2)/A^2}<BR>\n" );
document.write( "=SQRT(4-1)/1=SQRT(3)<BR>\n" );
document.write( "B*E=2SQRT(3)<BR>\n" );
document.write( "B/E=2/SQRT(3)<BR>\n" );
document.write( "FOCI ARE (H,K+BE) AND (H,K-BE)<BR>\n" );
document.write( "(1,2SQRT(3)) AND (1,-2SQRT(3))<BR>\n" );
document.write( "DIRECTRIX ARE.Y=K+B/E AND K-B/E<BR>\n" );
document.write( "Y=2/SQRT(3)..AND...Y=-2/SQRT(3)<BR>\n" );
document.write( "GRAPH IS GIVEN BELOW...<BR>\n" );
document.write( "graph( 500, 500, -3, 3, -3, 3,<BR>\n" );
document.write( "(4-4*(x-1)^2)^0.5,-(4-4*(x-1)^2)^0.5) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );