Quick thread -How much derivation in Parametric Equations of Parabola is required? (1 Viewer)

[blackops23]

Ok, just wondering, in general, any question you get relating to Parametric Equations of Parabola, what specifics can you simply STATE in your solution, and what specifics MUST you DERIVE in your solution.

I.e. I definitely know you have to derive points of intersection of tangents/normals. But what about the equations of chords of contacts, focal chords, tangents/ normals - Can I just state their generic equation in my solution( e.g y= tx - at^2), or do I have to derive them??

Thanks guys

 

[slyhunter]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

My teacher says you're allowed to quote them if you're not asked to do derive them (he's a HSC marker). But it's better to derive because I find it's easier to remember the derivation rather than the actual equation.

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

My teacher says you're allowed to quote them if you're not asked to do derive them (he's a HSC marker). But it's better to derive because I find it's easier to remember the derivation rather than the actual equation.

find that hard to believe



Anything that is not given in the question should be derived. Some questions will say stuff like "The equation of the tangent at p is y =..... ( DO NOT PROVE THIS ) " then they will go to talk about other stuff. I am pretty sure the rule would be unless it tells you NOT to derive, then you must derive it

 

[slyhunter]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

Eh, personally I derive it.

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

for exam, in the 2010 3unit a question was:

The tangent to the parabola at P, y = px − ap2, meets the y-axis at L.
The point M is on the directrix, such that PM is perpendicular to the directrix.
Show that SLMP is a rhombus.


. In this case you dont need to derive the eqn of the tangent, as it was given in the question

 

[blackops23]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

find that hard to believe



Anything that is not given in the question should be derived. Some questions will say stuff like "The equation of the tangent at p is y =..... ( DO NOT PROVE THIS ) " then they will go to talk about other stuff. I am pretty sure the rule would be unless it tells you NOT to derive, then you must derive it

So say like it says, an equation cuts the parabola x^2 = 16y at P and Q, with parameters p and q. Find the point of intersection of the tangents at P and Q.
So would I have to:

1.Solve the two equations to get P and Q (well of course I have to do this)
2. Find the dy/dx of the parabola, sub in the x-coordinates of P and Q.
3. Use these gradients to derive the equations of the tangents at P and Q.
4.Then solve these two equations to find the intersection point.

Instead of doing all that, can't I just state the general form of the tangent, i.e. y=tx - at^2, and then solve the two to get the P.O.I?? Would I lose marks if I skipped the derivation of tangents/normals/chord of contacts etc??

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

Yes you most likely would lose marks if you just wrote down y = tx - at^2 , also out of curiousity where did you get these questions from , jones and couchman book??

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

yes you would have to derive the tangent, of course, the question would be like 2 easy marks in a 3unit exam, just to catch out the 4unit students that are not strong at 2unit .

would pop up in like Q2 or Q3.

in fact that could even be a 2unit question, what are you complaining about, should take like 1minute to derive the eqn of tangent from first principles

 

[blackops23]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

Yes you most likely would lose marks if you just wrote down y = tx - at^2 , also out of curiousity where did you get these questions from , jones and couchman book??

Yeah J&C, guess that's why they are so easy compared to HSC ext 1 exams, but its good for drilling in...

Also 1 minute is really huge in an exam, everysingle seconds counts...

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

Also 1 minute is really huge in an exam, everysingle seconds counts...

not for 2 easy marks out of 84

 

[khfreakau]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

I think it's implied, but you can tell. You may ONLY state/assume the general form of the tangent if its given. This is standard for anything in parametrics/conics. You are only allowed to quote what they give you for questions from these topics. Otherwise, you ALWAYS have to derive, or else you'll lose marks. This comes from my teacher who marked the MX1 exam last year...

 

[cutemouse]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

yes you would have to derive the tangent, of course, the question would be like 2 easy marks in a 3unit exam, just to catch out the 4unit students that are not strong at 2unit .

You honestly don't think 4U students would know how to derive the equation of a tangent? LOL

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

You honestly don't think 4U students would know how to derive the equation of a tangent? LOL

well I know one that couldnt solve simultaneous eqns, so anythings possible

 

[cutemouse]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

well I know one that couldnt solve simultaneous eqns, so anythings possible

Yeah except for the fact that you do similiar or harder variations of parametrics in conics, a 4U topic. So it's a topic that 4U students would probably be advantaged at if anything... Smart one dumbo

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

Yeah except for the fact that you do similiar harder variations of parametrics in conics, a 4U topic. So it's a topic that 4U students would probably be advantaged at if anything... Smart one dumbo

why do you keep picking fights afro man??

you still cant accept the fact that my point is 100% correct. There are some people ( yourself included ) that did 4unit and yet cant do a 2unit question. Still dont have a clue why you asked the 2unit question in the feburary after the 2009 HSC, uni wasnt even back by then.

So one thinks either you were tutoring someone and you couldnt figure out that question (lol) , or you were doing a bridging course in maths at uni and all this crap bout you doing 4unit is a lie, or third option is that you actually did do 4unit but forgot your 2unit.

Seriously, Why do you keep bringing up my point, its obviously valid and correct yet you still want to keep fighting it.

give it up you stubborn bastard, admit that im right and leave it alone.

You couldnt do a basic 2unit question with simultaneous eqns , and you did 4unit.

understand how you are wrong kiddo , and how my statement about 4unit students not knowing 2unit material is right ?

 

[cutemouse]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

you still cant accept the fact that my point is 100% correct.

And you can't seem to accept the fact that 4U students can find the equation of a curve and that Parametrics is basically a watered down version of conics. Note that the parabola is a conic with eccentricity 1.

Still dont have a clue why you asked the 2unit question in the feburary after the 2009 HSC, uni wasnt even back by then.

FYI that was a Year 8 / Junior maths question and I asked it to see what type of responses I'd get.

4U students certainly perform better in the 3U part of the course. So your point is skewed.

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

And you can't seem to accept the fact that 4U students can find the equation of a curve and that Parametrics is basically a watered down version of conics. Note that the parabola is a conic with eccentricity 1.


FYI that was a Year 8 / Junior maths question and I asked it to see what type of responses I'd get.

4U students certainly perform better in the 3U part of the course. So your point is skewed.

Another thing 4unit maths creates, arrogance, you are unable to accept that you are wrong.

 

[cutemouse]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

Another thing 4unit maths creates, arrogance, you are unable to accept that you are wrong.

Coming from someone that can't even prove the Wallis product

 

[Bored Of Fail 2]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

Coming from someone that can't even prove the Wallis product

lol k man.

do you need me to get you a definition of arrogance so I can show you how my statement is substantiated by your actions

 

[cutemouse]

Re: Quick thread -How much derivation in Parametric Equations of Parabola is required

lol k man.

do you need me to get you a definition of arrogance so I can show you how my statement is substantiated by your actions

Come back when you can prove the wallis product