Rivalry's Parametrics Troubles (1 Viewer)

[RivalryofTroll]

I got answers but not too sure if it's right so wanted to confirm:

Find the Cartesian equation of the following set of points:

1. [a(p+q), apq], given that p - q = 1 + pq

My answer:
x^2 - a^2 = y(y+6a)

2. [t - (4/t), (t^2/2) + (8/t^2)]

My answer:
x^2 = 2(y-4)

 

[My Name is Khan]

Correct

LOLOLOL

 

[nightweaver066]

If you want to check, sub in the point.

 

[RivalryofTroll]

P(2ap, ap^2) Q (2aq, aq^2)

x^2 = 4ay

PQ is a focal chord. I.e. pq = -1

Question: If R is the P.O.I of the tangents at P, Q and M is the midpoint of PQ, prove that the parabola bisects the interval RM.

SO I found intersection of tangents to be R [a(p+q), apq] and the midpoint M [a(p+q), [a(p^2 +q^2)]/2]

What do I do next?

 

[nightweaver066]

Find the midpoint of RM and sub the x-coordinate into the parabola and if you get the corresponding y-coordinate, the parabola bisects interval RM.