Conics Question (2 Viewers)

[tommykins]

Posted this up in another thread ( to ironically avoid making another thread ) but it got deleted.

There are three points of a rectangular hyperbola xy = c² . P,Q and R with parametric values given by p,q, and r.
The tangents at P(cp,c/p) and Q intersect each other at the point T, while the chord PQ is parallel to the tangent at R.

i)Show that p/r = r/q
ii) If T is (2cpq/p+q, 2c/p+q), show that O, T, R form a straight line.

I could do ii) simply, but i) has me stumped and I have no idea where to start.

 

[conics2008]

Hey this is simple =)

It goes like this

Gradient of PQ = -1/pq and gradient at point R is -1/r^2 right

since you said they are parallel... therefore

-1/pq=-1/r^2

take off the negatives

you are left with r^2 = pq >> divide each side by r and q

you get p/r = r/q =)

 

[conics2008]

With conics you mainly need to play around with them, and try your best to make it look like what they ask you at all cost.....

This has been my method for all the proving or showin question.. do what ever ( that is chuck numbers, take off numbers God knows what, just make it look like what they ask you )

 

[tommykins]

Hey this is simple =)

It goes like this

Gradient of PQ = -1/pq and gradient at point R is -1/r^2 right

since you said they are parallel... therefore

-1/pq=-1/r^2

take off the negatives

you are left with r^2 = pq >> divide each side by r and q

you get p/r = r/q =)

Ahh, thing was I had no idea what p/q etc. are, so it got me lost.

Makes perfect sense though. Thank you.