Locus Help (1 Viewer)

Lukybear

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Parabola x=2at, y=at^2 has parameters p, q etc..
M is mid point of chord PQ, T is point on parrabola where tangent is parrallel to PQ and I is point where the tangents at P and Q intersect

M,T,I lie on a vertical line, with T the mid point of MI
The tangent at T bisects tangents PI and QI

What is the ratio of the areas of Triangle PQI and PQT
 

kcqn93

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i got some strange looking answer:

PQI : PQT

= 2[(p-q)^2 - 2p^2] : (p-q)^2 - 4p^2

which looks wrong.... whats the answer?
 
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