Conics Hyperbola Question (1 Viewer)

[namelyanonymous]

I have no idea what I'm doing wrong with this question:

P( p, 1/p) and Q (q, 1/q) are two varibale points on the rectangular hyperbola xy = 1.
a) If M is the midpoint of the chord PQ and OM is perpendicular to PQ, express q in terms of p

I found:

M = ((p+q)/2, (p+q)/2pq)
m(OM) = 1/pq
m(PQ) also turns out to be 1/pq

Since the gradients are equal, they're parallel not perpendicular. What am I doing wrong?

Thanks in advance!

 

[Sy123]

I have no idea what I'm doing wrong with this question:

P( p, 1/p) and Q (q, 1/q) are two varibale points on the rectangular hyperbola xy = 1.
a) If M is the midpoint of the chord PQ and OM is perpendicular to PQ, express q in terms of p

I found:

M = ((p+q)/2, (p+q)/2pq)
m(OM) = 1/pq
m(PQ) also turns out to be 1/pq

Since the gradients are equal, they're parallel not perpendicular. What am I doing wrong?

Thanks in advance!

Redo your working for m(PQ), it should turn out to be -1/pq

Which means that p=1/q (since -1/pq * 1/pq = -1)

 

[namelyanonymous]

Redo your working for m(PQ), it should turn out to be -1/pq

Which means that p=1/q (since -1/pq * 1/pq = -1)

Oh my god! I found it like three times and all those times I completely forgot to keep the negative in I'm so stupid ugh.

Thanks again!

Also, I guess it would be +/- 1/q as opposed to 1/q?

 

[Sy123]

Oh my god! I found it like three times and all those times I completely forgot to keep the negative in I'm so stupid ugh.

Thanks again!

Also, I guess it would be +/- 1/q as opposed to 1/q?

Yep you are correct haha