Easy question (1 Viewer)

[NEGROizzle]

Hey,

I just had my 4u test today and I'm just a bit anxious and was wondering if you guys could help me out with this question.

P and Q are points on xy = c^2

P(cp,c/p) & Q(cq,c/q)

tangents meet at T, find the locus of T if pq = 1 AND THE RESTRICTIONS of the locus.

thanksss ;D

 

[saj72]

you fkd up niggerizzle, its pq = -1

 

[NEGROizzle]

na pretty sure it was pq = 1 saj LOL

 

[Affinity]

let T = (x,y) then

(x-cp) + p^2 (y - c/p) = 0
x + (p^2)y = 2cp
x + (q^2)y = 2cq

x = 2c / (p+q)
y = 2cpq/(p+q) = 2c / (p+q) = 2c / (p + 1/p)

so the line's x=y , x in [-c,c]

as p + 1/p >= 2 or p + 1/p <= -2

EDIT: thought about it again

if we allow p = q then it's the above line segment + 2 lines perpendicular to the segment passing through (c,c) and (-c,-c).
if you do not allow p = q then it's the line segment from bu with x in the open interval (-c,c)