document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35337>Question 35337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  graph x-3= -1/8(y+2)^2. Write the coordinates of the vertex and the focus and the equation of the directrix.<BR>\n" );
document.write( "2.Find all solution to each system of equations algerbaiclly.<BR>\n" );
document.write( "   x^2 + y^2 =25<BR>\n" );
document.write( "   3x^2 +  2y^2 = 59<BR>\n" );
document.write( "3. Write the standard equations of the conic section with the given characteristics<BR>\n" );
document.write( "   hyperbola with foci at (5,-7) and (14,0) and vertices at (12,0) and (4,0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21466 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=21466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  1.  graph x-3= -I/8 (y=2)^2. Write the coordinates of the vertex and<BR>\n" );
document.write( "> the<BR>\n" );
document.write( "> > > focus and the equation of the directrix.<BR>\n" );
document.write( "X-3=-(1/8)(Y-2)^2<BR>\n" );
document.write( "(Y-2)^2=-8(X-3)<BR>\n" );
document.write( "COMPARING WITH STD.EQN.OF PARABOLA<BR>\n" );
document.write( "(Y-K)^2=4A(X-H)^2...WE GET <BR>\n" );
document.write( "VERTEX=(H,K)=(3,2)<BR>\n" );
document.write( "A=-2<BR>\n" );
document.write( "FOCUS =(H+A,K)=(3-2,2)=(1,2)<BR>\n" );
document.write( "DIRECTIX IS  ... X-H+A=0...THAT IS<BR>\n" );
document.write( "X-3-2=0...OR...X=5<BR>\n" );
document.write( "GRAPH IS GIVEN BELOW \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+10%2C+-10%2C+10%2C2%2B%28-8%2Ax%2B24%29%5E0.5%2C2-%28-8%2Ax%2B24%29%5E0.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "> > >  2.Find all solution to each system of equations algerbaiclly.<BR>\n" );
document.write( "> > >     x^2 + y^2 =25<BR>\n" );
document.write( "SINCE SUM OF TWO SQUARES = 25 ,AND SQUARES ARE ALWYS POSITIVE ,WE GET THE SOLUTION SETS AS X^2<=25 AND Y^2<=25....THAT IS<BR>\n" );
document.write( "1.0<=|X|<=5 AND 0<=|Y|<=5<BR>\n" );
document.write( "> > >     3x^2 +  2y^2 = 59...YOU CAN DO THE SAME WAY AS ABOVE<BR>\n" );
document.write( "3X^2<=59 AND 2Y^2<=59..ETC.......<BR>\n" );
document.write( "> > > 3. Write the standard equations of the conic section with the given <BR>\n" );
document.write( "> > > characteristics<BR>\n" );
document.write( "> > >     hyperbola with foci at (5,-7) and (14,0) and vertices at (12,0) and<BR>\n" );
document.write( "> > > (4,0)<BR>\n" );
document.write( "STANDARD EQN.OF HYPERBOLA IS <BR>\n" );
document.write( "(X-H)^2/A^2 -(Y-K)^2/B^2 =1...WHERE<BR>\n" );
document.write( "CENTRE IS (H,K)...WE ARE GIVEN VERTICES ARE AT (12,0) AND (4,0)...SO CENTRE IS AT<BR>\n" );
document.write( "(12+4)/0,(0+0)/2=(8,0)<BR>\n" );
document.write( "HENCE H=8....K=0<BR>\n" );
document.write( "TRANSVERSE AXIS IS Y=K=0<BR>\n" );
document.write( "LENGTH OF TRANVERSE AXIS =2A=16<BR>\n" );
document.write( "A=8<BR>\n" );
document.write( "CONJUGATE AXIS IS X=H=8<BR>\n" );
document.write( "PLEASE CHECK DATA....CENTRE WHICH IS MID POINT OF FOCI AND ALSO MIDPOINT OF VERTICES ARE NOT TALLYING </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );