document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35524>Question 35524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sketch  and find the equation<BR>\n" );
document.write( "Foci=(2,6) and (2,-6)<BR>\n" );
document.write( "difference in focal radii is 4\r<BR>\n" );
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document.write( "that is all the information that it gives me. and i have to sketch and find the equation using that information </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22604 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=22604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WE HAVE TO ASCERTAIN THE FOLLOWING FIRST<BR>\n" );
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document.write( "Focal Radius\r<BR>\n" );
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document.write( "This term has distinctly different definitions for different authors.\r<BR>\n" );
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document.write( "Usage 1: For some authors, this refers to the distance from the center to the focus for either an ellipse or a hyperbola. This definition of focal radius is usually written c.\r<BR>\n" );
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document.write( "Usage 2: For other authors, focal radius refers to the distance from a point on a conic section to a focus. In this case the focal radius varies depending where the point is on the curve (unless the conic in question is a circle). If there are two foci then there are two focal radii.\r<BR>\n" );
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document.write( "Note: Using this second definition, the sum of the focal radii of an ellipse is a constant. It is the same as the length of the major diameter. The difference of the focal radii of a hyperbola is a constant. It is the distance between the vertices.<BR>\n" );
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document.write( "NOW ON TO YOUR PROBLEM<BR>\n" );
document.write( "sketch and find the equation<BR>\n" );
document.write( "Foci=(2,6) and (2,-6)<BR>\n" );
document.write( "difference in focal radii is 4<BR>\n" );
document.write( "that is all the information that it gives me. and i have to sketch and find the equation using that information<BR>\n" );
document.write( "SINCE THE DIFFERENCE IN FOCAL RADII IS GIVEN TO BE CONSTANT LET US TAKE IT AS HYPERBOLA BY THE SECOND DEFINITION.<BR>\n" );
document.write( "IN WHICH CASE DIFFERENCE IN FOCAL RADII=2B=4...B=2<BR>\n" );
document.write( "FOR THE STD.EQN.OF HYPERBOLA WE HAVE <BR>\n" );
document.write( "(Y-K)^2/B^2-(X-H)^2/A^2=1....WE HAVE<BR>\n" );
document.write( "FOCI ARE {H,K+BE} AND {H,K-BE}....H=2....K+BE=6...K-BE=-6...HENCE K=0 AND BE=6<BR>\n" );
document.write( "SINCE B=2...E=6/2=3<BR>\n" );
document.write( "WHERE E IS<BR>\n" );
document.write( "ECCENTRICITY<BR>\n" );
document.write( "=SQRT{(A^2+B^2)/B^2}=3...SQUARING<BR>\n" );
document.write( "9=(A^2+4)/4<BR>\n" );
document.write( "36=A^2+4<BR>\n" );
document.write( "A^2=36-4=32<BR>\n" );
document.write( "HENCE EQN.OF HYPERBOLA IS <BR>\n" );
document.write( "Y^2/4- (X-2)^2/32=1<BR>\n" );
document.write( "GRAPH IS <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-20%2C+25%2C+-10%2C+10%2C2%2A%281%2B%28%28x-2%29%5E2%2F32%29%29%5E0.5%2C+%28-2%29%2A%281%2B%28%28x-2%29%5E2%2F32%29%29%5E0.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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