• Congratulations to the Class of 2024 on your results!
    Let us know how you went here
    Got a question about your uni preferences? Ask us here

Yr 11 Ext Topic: Parametrics (1 Viewer)

st1m

Member
Joined
Mar 29, 2008
Messages
60
Gender
Male
HSC
2009
Ok I have my maths ext 1 exam tommorow and parametrics is worth 12 marks out of the 84. It's probably the only ext topic that i have no clue of what to do.:uhoh:

Can someone please help, notes and explainations of 1 parameter and 2 parameters? i need urgent help as our teacher didn't explain them properly.:mad:

Thanks:rolleyes:
 
Joined
Sep 9, 2008
Messages
247
Gender
Female
HSC
2009
well for parabola x^2 = 4ay parameters are:
x = 2at
y = at^2

e.g. x^2 = 12y
therefore a= 3 so parameters are:
x = 6t
y = 3t^2

stuff from my study notes that may help:

Parametric representation of the parabola:
- Parameters:
- The use of a third variable is often used to simplify a proof. Many cartesian equations may be represented with a set of parametric equations.
- Parametric representation of x²= 4ay
- The parametric equations for basic parabola x²= 4ay are: x= 2at, y = at²
- The equation of the chord:
- Standard points P (2ap, ap²) and Q (2aq, aq²)
- Use two point formula for the equation of a line.
- Focal chords:
- The condition of a chord to be a focal chord is that: pq = -1
- Tangents and normals to x²=4ay at point P with parameter P:
- Gradient of tangent = p, gradient of normal = -1/p
- Equation of tangent: y= px – ap²
- Equation of normal = x + py = ap3 + 2ap
 

st1m

Member
Joined
Mar 29, 2008
Messages
60
Gender
Male
HSC
2009
thankyou so much melisoverschool
what about the point of intersection stuff?

thnx anyways i will copy this stuff down.
 

jellybelly59

Active Member
Joined
Oct 13, 2007
Messages
1,382
Location
where there is pho and sugar cane drinks
Gender
Male
HSC
2009
The tangents to the parabola x^2 = 4ay at points P and Q intersect at the point ( [a(p+q)] , [apq] )

The normals to the parabola x^2 = 4ay at points P and Q intersect at the pt

( [-apq(p+q)] , [a((p^2)+pq+(q^2)+2)]
 

tommykins

i am number -e^i*pi
Joined
Feb 18, 2007
Messages
5,730
Gender
Male
HSC
2008
回复: Re: Yr 11 Ext Topic: Parametrics

You won't get very far if all you do is remember formulas. Half the time they ask you to derive it anyways.
 

lyounamu

Reborn
Joined
Oct 28, 2007
Messages
9,998
Gender
Male
HSC
N/A
jellybelly59 said:
The tangents to the parabola x^2 = 4ay at points P and Q intersect at the point ( [a(p+q)] , [apq] )

The normals to the parabola x^2 = 4ay at points P and Q intersect at the pt

( [-apq(p+q)] , [a((p^2)+pq+(q^2)+2)]
Yeah, don't memorise it as tommykins said.

It's just best to practise how to derive them.

I bet you got them from excel prelim mx1.
 

jellybelly59

Active Member
Joined
Oct 13, 2007
Messages
1,382
Location
where there is pho and sugar cane drinks
Gender
Male
HSC
2009
lyounamu said:
Yeah, don't memorise it as tommykins said.

It's just best to practise how to derive them.

I bet you got them from excel prelim mx1.
no i actually got it from the maths in focus hsc ext. 1 book 2... I know how to derive it's just that i have a parametrics test and she told us to study it for the 3 unit exam
 

clintmyster

Prophet 9 FTW
Joined
Nov 12, 2007
Messages
1,067
Gender
Male
HSC
2009
Uni Grad
2015
just read through the examples in the textbook and notice the techniques they use to get the tangent of a chord or what they do with the focus. Knowing how to differentiate helps as well. Other than that if you need some questions on parametrics, feel free to ask me to post them
 
Joined
Sep 9, 2008
Messages
247
Gender
Female
HSC
2009
Re: 回复: Re: Yr 11 Ext Topic: Parametrics

tommykins said:
You won't get very far if all you do is remember formulas. Half the time they ask you to derive it anyways.
yeah i know i had to do it my extension prelim but it was just a summary to give him some ideas and a basic overview. i wasn't going to spend ages typing up the whole thing he should be able to derive it himself
 
Last edited:

youngminii

Banned
Joined
Feb 13, 2008
Messages
2,083
Gender
Male
HSC
2009
It's nice to have a basic outline of the formulas though
So if they ask you to derive one, you can do it quicker than if you didn't know
I love parametrics, so logical
 

tommykins

i am number -e^i*pi
Joined
Feb 18, 2007
Messages
5,730
Gender
Male
HSC
2008
回复: Re: Yr 11 Ext Topic: Parametrics

youngminii said:
It's nice to have a basic outline of the formulas though
So if they ask you to derive one, you can do it quicker than if you didn't know
I love parametrics, so so logical

Lol, as opposed to what other branch of mathematics? :p
 

youngminii

Banned
Joined
Feb 13, 2008
Messages
2,083
Gender
Male
HSC
2009
Re: 回复: Re: Yr 11 Ext Topic: Parametrics

tommykins said:
Lol, as opposed to what other branch of mathematics? :p
OH I KNOW THIS
I KNOW THIS
Umm.. Sequences and Series (or at least what I've done so far)
All we do is remember the formulas and plug it in =X
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top