Parametric Formulae (1 Viewer)

[Trebla]

I've repeatedly derived so many formulas when doing exercises involving parametric representation. I'm so sick of that repetitive deriving that I often shove in some formulas I proved before and stick with that rather than deriving that equation/formula that I used to save time. I know that some of these 'identities' cannot be assumed and must be derived when it comes to exams, but I want to know which parametric identities are we allowed to use or assume without having to derive them, in exams.
e.g. I think that we can assume the gradient of a tangent to point P(2ap,ap²) is always p (similarly for Q.....), but can someone please clarify on that?

 

[acmilan]

If you want my opinion, I wouldnt test the marker in an exam. If you do it the full way, you can be certain of the marks. However when doing questions at home its really up to you. As far as I can see from a quick look at the syllabus, there is no mention on what you can/cant assume, other than the parametric equation of the parabola.

 

[Riviet]

e.g. I think that we can assume the gradient of a tangent to point P(2ap,ap²) is always p (similarly for Q.....), but can someone please clarify on that?

Yes, that one is allowed, just make sure you state it out when doing a question ie "gradient of tangent at (2ap,ap²) is p. I'm not sure about the others, post some more examples of formulas in.

P.S I dislike this topic.

 

[pLuvia]

Is parametrics a year 12 topic? or preliminary? either way we haven't learnt it

 

[Riviet]

It is explicitly a 3u topic, and is usually done sometime this term. My school decided to do it late last term and finished 1st week this term.
I don't like it...

 

[pLuvia]

It is explicitly a 3u topic, and is usually done sometime this term. My school decided to do it late last term and finished 1st week this term.
I don't like it...

I learnt it at tutor but like it's hard to grasp

 

[acmilan]

Its a prelim topic, or was for me at least.

 

[nick1048]

Its a prelim topic, or was for me at least.

same. Parametrics is good to attempt after the motion stuff like projectiles and SHM

 

[Sparcod]

Is parametrics a year 12 topic? or preliminary? either way we haven't learnt it

We have in prelim. p is pretty much an unknown. a is a constant and x and y are variables.

 

[Riviet]

it's hard to grasp

I reckon!!! That's one of the reasons why alot of students dislike parametrics.

 

[HamuTarou]

but once u grasp it, it's not that hard to do the questions (if u know to prove the eqt of tang, norm, chord...etc)

 

[Trebla]

post some more examples of formulas in.

Here's some:
- Equation of tangent at (2at,at²) is y = xt - at
- Equation of normal at (x1,y1) is y - y1 = (-2a/x1)(x - x1)
- Equation of chord joining P(2ap,ap²) and Q(2aq,aq²) is y = (p + q)x/2 - apq
- If PQ is a focal chord of P(2ap,ap²) and Q(2aq,aq²), then pq = -1
- Equation of chord of contact of tangents drawn from external point (x1,y1) is x.x1 = 2a(y + y1)
- Equation of normal at P(2ap,ap²) is x + py = ap³ + 2ap
- The length of the latus rectum of a parabola is 4a

 

[klaw]

I'd say it depends on the wording of the Q and the mark allocation. E.g. if it says "Show that" then you derive it, but if you're finding a locus or something then you probably won't lose marks for not deriving.

 

[Riviet]

At least be able to derive those that you have listed, and be aware of their existence so when a question asks about them, you'll have an idea of what you're supposed to end up deriving