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Show that normals to the rectangular hyperbole xy=cc at the point (t) meets the Curve again at a point (t`) such that t*t*t*t`=-1.

Show that normals to the rectangular hyperbole xy=cc at the point (t) meets the Curve again at a point (t`) such that t*t*t*t`=-1.

Grade:12th pass

1 Answers

Vikas TU
14149 Points
5 years ago
 Condition of ordinary at t is xt3 − yt − ct4 + c = 0 
it goes through (ct' , c/t') 
=> ct't3 − c/t't − ct4 + c = 0 
=> (t3t' + 1) (t'− t) = 0 
=> t3t' = −1 

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