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![[Post New]](/templates/default/images/icon_minipost_new.gif) 2 Dec 2007 22:08:55 IST
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prove that locus of mid pts of normal chords of y2=4ax is y2/2a + 4a3/y2 = x-2a
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there are numerous options besides I.I.T
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2 Dec 2007 23:01:38 IST
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eqn of chord whose mid point is (h, k) is
ky-2a(x+h) = k^2-4ah
now eqn of normal at point (at^2, 2at) is
y+tx=2at+at^3
compare the coeff of x and y and eliminate t to get the locus
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2 Dec 2007 23:11:10 IST
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u'll get
k/1 = -2a/t = k^2-2ah/2at+at^3
t=-2a/k
k=(k^2-2ah)/(2at+at^3) put t=-2a/k
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2 Dec 2007 23:11:27 IST
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u'll get
k/1 = -2a/t = k^2-2ah/2at+at^3
t=-2a/k
k=(k^2-2ah)/(2at+at^3) put t=-2a/k
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But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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