"equation of chord to the hyperbold xy=c^2" (rectangular hyperbola) (1 Viewer)

[dawso]

gday all, bloody tryin 2 derive this equation but am stuck and all textbooks as usual just skip fifty steps and have the answer (patel is worst culprit here)

anyway, can someone help em derive this in cartesian form?, so far i got...

let p(x1, y1) and G(x2, y2) lie on xy = c^2

gradient of PQ is

m=(y2 - y1) / (x2-x1)

both books i got just skip to -c^2/x1x2....help please???

 

[dawso]

lol, dw guys, i got it

 

[FinalFantasy]

gday all, bloody tryin 2 derive this equation but am stuck and all textbooks as usual just skip fifty steps and have the answer (patel is worst culprit here)

anyway, can someone help em derive this in cartesian form?, so far i got...

let p(x1, y1) and G(x2, y2) lie on xy = c^2

gradient of PQ is

m=(y2 - y1) / (x2-x1)

both books i got just skip to -c^2/x1x2....help please???

x1,y1 lies on xy=c²
so y1=c²\x1, same for the y2....
m=(y2 - y1) / (x2-x1)
=[c²\x2-c²\x1]\(x2-x1)
=[(x1c²-x2c²)\x1x2] \(x2-x1)
=[-c²(x2-x1)\x1x2]\(x2-x1)
=-c²\x1x2
eq. of chord PQ:
(y-y1)\(x-x1)=-c²\x1x2
x1x2y-x1x2y1=-c²x+c²x1
x1x2y-x2c²=-c²x+c²x1
c²x+x1x2y=c²(x1+x2)