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# rectangular hyperbola's beautiful meeting points watch

1. say you have point P(cp,c/p) and Q (cq,c/p) where p not equal to -q, and assuming that they lie on xy=4, how do you figure what point P and Qs tangents meet at?

I have done some working out and figured that

x = (4pq^2 - 4p^q) / (q^2 - p^2)

and

y = (4q - 4p) / (q^2 - p^2)

x = 4pq / (p + q) and

y = 4 / (p + q)

Can anyone tell me how "they" manage to get the answer to what they got the answer as?
2. (Original post by lesser weevil)
say you have point P(cp,c/p) and Q (cq,c/p) where p not equal to -q, and assuming that they lie on xy=4, how do you figure what point P and Qs tangents meet at?

I have done some working out and figured that

x = (4pq^2 - 4p^q) / (q^2 - p^2)

and

y = (4q - 4p) / (q^2 - p^2)

x = 4pq / (p + q) and

y = 4 / (p + q)

Can anyone tell me how "they" manage to get the answer to what they got the answer as?
nb the difference of two squares - then teh denominator and numerator cancel to what is desired

gald to be of service

pk
3. (Original post by Phil23)
nb the difference of two squares - then teh denominator and numerator cancel to what is desired

gald to be of service

pk
DARN, am I STUPID, or WHAT?

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