Parametric Normals question (1 Viewer)

[Chris100]

P and Q are the points t=p and t=q on the parabola x=2at, y=at²

There was a question asking me to find the equation of the normals at to the curve at P and Q

Then this: Prove that p³-q³=(p-q)(p²+pq+q²)

By proving, I assume that I have to use the normals to work this out, but in case I assumed wrong; am I allowed to prove this by just expanding RHS and say that it equals LHS?

 

[QZP]

Someone asked this question before. I believe the consensus was that the question was not related to the parabola. Just do expanded RHS = LHS

 

[rumbleroar]

Someone asked this question before. I believe the consensus was that the question was not related to the parabola. Just do expanded RHS = LHS

+1
that's what my teacher said too

 

[enigma_1]

LOOOL Chris yeah I did ask this question a while ago hahaha but nah you don't need to use the normals to work it out. Weird question, I know. Cambridge ay?

 

[braintic]

The thing is, it is true for ALL values of p and q. It is an algebraic identity, and should be recognised as such from early year 11 algebra.
As such, there could not possibly be any geometric relationship to do with the parabola, normals, etc that would lead to a proof of the identity.