Yr 11 Ext Topic: Parametrics (1 Viewer)

[st1m]

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.

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.

Thanks

 

[Melisoverschool]

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]

thankyou so much melisoverschool
what about the point of intersection stuff?

thnx anyways i will copy this stuff down.

 

[jellybelly59]

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]

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]

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]

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]

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

 

[Melisoverschool]

Re: 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.

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

 

[youngminii]

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]

回复: Re: Yr 11 Ext Topic: Parametrics

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?

 

[youngminii]

Re: 回复: Re: Yr 11 Ext Topic: Parametrics

Lol, as opposed to what other branch of mathematics?

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