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![[Post New]](/templates/default/images/icon_minipost_new.gif) 26 Apr 2007 12:26:43 IST
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Q. find the locus of the mid points of the chords of the hyperbola x2/a2 - y2/b2 = 1 which subtend a right angle at the origin
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26 Apr 2007 12:28:43 IST
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please answer
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26 Apr 2007 12:41:09 IST
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somebody please telll
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26 Apr 2007 12:49:35 IST
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same method as in this
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26 Apr 2007 12:52:35 IST
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can u tell me when and why here do we homogenise ?
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26 Apr 2007 13:00:40 IST
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Let the mid-point be (h,k).
Equation of chord with mid point (h,k) is given by :
T = S1
xh/a2 - yk/b2 - 1 = h2/a2 - k2/b2 - 1
Make this equation of chord homogeneous with the curve x2/a2 - y2/b2 = 1 and since the chord subtends a right angle at (0,0) apply :
coefficient of x2 + coefficient of y2 = 0
This will give you the required locus.
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Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur
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26 Apr 2007 13:24:16 IST
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Let the mid-point be (h,k).
Equation of chord with mid point (h,k) is given by :
T = S1
xh/a2 - yk/b2 - 1 = h2/a2 - k2/b2 - 1
Make this equation of chord homogeneous with the curve x2/a2 - y2/b2 = 1 i.e x2/a2-y2/b2=(xh/a2 - yk/b2)2/(h2/a2 - k2/b2 )2 1/a2(h2/a2 - k2/b2 )2x2-1/b2(h2/a2 - k2/b2 )2 y2 = h2/a4 x2+ k2/b4 y2-2hk/a2b2 the lines are perpendicular if coefficient of x2 + coefficient of y2 = 0 i.e 1/a2(h2/a2 - k2/b2 )2 -h2/a4 -1/b2(h2/a2 - k2/b2 )2 - k2/b4 =0 (h2/a2 - k2/b2 )2(1/a2-1/b2)=h2/a4 +k2/b4 hence the locus by putting x=h and y=k
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26 Apr 2007 13:34:57 IST
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aternate method if u r not comfortable hy homonoginizing..... after writing the general equation by T=S1 just check out for something visible, like the distance from origin ,its intercepts ,etc write this eqution in perpendicular form u'll get length of perpendicular = ab/(a^2+b^2)^(1/2) (a^2+b^2)(h^2/a^2-k^2/b^2)^2=(ab)^2*(h^2/a^4+K^2/b^4)
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26 Apr 2007 16:00:49 IST
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yaar...can u please tell me by the homonizing method in a little detail please ...
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26 Apr 2007 16:52:10 IST
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please help with this concept of homonizing ....pls frenz
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26 Apr 2007 17:17:31 IST
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???????????????
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26 Apr 2007 17:53:21 IST
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Homogenising means to make the degree of each term of the conic same...
this is done by considering x=x.1 if degree is2..x=x.1^2 if degree is 3...
and then replace 1 from the eq with which u hv to homogenise by taking x and y terms to one side and dividing by constant term
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27 Apr 2007 20:23:42 IST
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I AM NOT ABLE TO UNDER STAND AN IOTA OF WHT'S WRITTEN, PLZ EXPLAIN IN AN EASY WAY AND ALSO HOMOGENISING WITH A SIMPLE EXAMPLE
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28 Apr 2007 18:40:56 IST
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