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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: PrinceOfPersia on January 17, 2013, 08:38:54 pm

Title: Parametric Equations
Post by: PrinceOfPersia on January 17, 2013, 08:38:54 pm: Hi everyone,
I'm really confused with parametric equations for circles,hyperbolas and ellipse, can any past students tell whether its vital to the course later on? Its because our school had never covered this topic and we were given it as holiday work. Also can anyone help me with its purpose and is there any helpful links which can help in learning it.
thanks alot :)
Title: Re: Parametric Equations
Post by: Stick on January 18, 2013, 11:39:19 am: I believe parametric equations are in the toolbox chapter of the Essentials textbook, implying it is assumed knowledge. Things in the toolbox chapter are not directly assessed, but may be required as a means of solving another type of problem. I guess you might get away with not learning it, but personally I wouldn't want to risk potentially ruling myself out of a question in the exam. :)
Title: Re: Parametric Equations
Post by: Conic on January 18, 2013, 02:33:14 pm: There was a parametric equations graph on last year's exam 2 as far as I remember.

Summary of my textbook:

Parametric: Cartesian:

$x=r*cos(t)+h$ and $y=r*sin(t)+k$ $(x-h)^2+(y-k)^2=r^2$

$x=a*cos(t)+h$ and $y=b*sin(t)+k$ $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

$x=a*sec(t)+h$ and $y=b*tan(t)+k$ $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

$x=a*csc(t)+h$ and $y=b*cot(t)+k$ $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

Also, to find the domain of the parametric function, graph each parameter as a function of y (eg if you have x=cos(t) and y=sin(t) over a limited domain, sketch y=cos(x) and y=sin(x)) and find the range that is common to both. That will be the domain of the parametric function.
Title: Re: Parametric Equations
Post by: PrinceOfPersia on January 18, 2013, 09:23:03 pm: Thanks alot, would regret not learning it if it comes up on the exam. :D
Title: Re: Parametric Equations
Post by: TrueTears on January 18, 2013, 09:36:53 pm: parametric equations are very very important, all of vector functions etc are related to parametric equations
Title: Re: Parametric Equations
Post by: Charmz on January 19, 2013, 12:14:10 am: Go back and look through year 11 material. It usually explains it a lot better since you first learn it in year 11. They do come up later on in the course and i guarantee they will appear in the exam.
Title: Re: Parametric Equations
Post by: BigAl on January 19, 2013, 01:28:38 pm: they are vital as you will need to apply chain rule afterwards (There was one question in 2011 exam 1 as well) I don't want to get you confused but all you have to do is make the trigonometric expressions alone. Then recognise a trigonometric identity and hence the curve
Title: Re: Parametric Equations
Post by: zvezda on January 19, 2013, 06:28:07 pm: They dont cover parametric equations in the essentials text for yr 11 do they ? I cant seem to find it
Title: Re: Parametric Equations
Post by: Charmz on January 19, 2013, 07:13:46 pm: Yeah they do. I don't remember what chapter but it's certainly in there somewhere.
Title: Re: Parametric Equations
Post by: PrinceOfPersia on January 20, 2013, 07:51:56 pm: We used the maths quest book for year 11 and that section is not in there. :-\
Title: Re: Parametric Equations
Post by: Conic on January 22, 2013, 03:00:18 am: just found this video that explains them very well: