Coordinate Geometry: Proving Chord & Tangent of Rectangular Hyperbola

[Harmony]

The points P(cp,c/p) and Q(cq,c/q) lie on the rectangular hyperbola xy=c^2. Show that the equation of the chord PQ is pqy+x=c(p=q), and deduce the equation of the tangent at the point P.

I can do the proving. And I can find the tangent as well if the word "deduce" is not there. How can you deduce the equation by referring to the chord PQ?

 

[Gokul43201]

- post deleted...I was talking out of my hat -

 

[HallsofIvy]

The points P(cp,c/p) and Q(cq,c/q) lie on the rectangular hyperbola xy=c^2. Show that the equation of the chord PQ is pqy+x=c(p=q), and deduce the equation of the tangent at the point P.

I can do the proving. And I can find the tangent as well if the word "deduce" is not there. How can you deduce the equation by referring to the chord PQ?

You mean pqy+ x= c(p-q). Remember that we can think of a tangent, at P, as being the "limit" of the chords as q goes to p. Take the limit as q goes to p of pqy+ x= c(p- q).