Parametrics Help (1 Viewer)

[hit patel]

Hey Guys Can you help Me understand Parametrics. I get locus and stuff but parametrics gets me to a mind blankout. I cant think at all when I do parametrics. I just dont know what I donot understand and when I look back at how to do that problem the answer is so simple. Eg: The Points Pand Q on curve x=2at and y=at^2 have parameters p and q respectively. a) Show that PQ intersects the directrix at (2a(pq-1)/(p+q),-a).
The answer to a was so simple that all u had to do was use the equation of chord and simultaneous the equation of directrix yet i failed to recognise that. b) Find point of intersection of a focal chord (pq=-1) and directrix.
Now all u had to do here was sub pq in the equation in part a) yet again i failed to recognise this. Complex numbers and other stuff such as integration etc seem so much simpler to me than this. Why Is this so? How can I actually become very good at this topic before my math 3u yearly exam approaching in 1 week.

Please Help. PLease Please. PLease. Going Crazy trying to get really good at this when I cant even get through the easiest ones.

 

[Study notes]

Try reading the proofs for the tangents, normals and chords I guess just remember the steps required to get to the certain form, the rest is just coordinate geometry stuff and algebra.

If that isn't the advice u were looking for, then keep practicing questions and ask someone to assist you. If you just can't see it at all... not sure what else u can do really. Keep practicing!

 

[obliviousninja]

I always suggest to draw a diagram before you begin, helps to understand things better.

 

[HeroicPandas]

Parametrics will always provide you will USEFUL information

eg. PQ is a focal chord, prove that ____ = ______

This means when u sub in the focus into chord PQ, it'll satisfy it and thus u will attain a CONDITION such as 'pq = -1'

All in all, FIND what they GIVE u

 

[SharkeyBoy]

I always suggest to draw a diagram before you begin, helps to understand things better.

YES, exactly this. Diagrams are soooooo helpful for me with locus q's

 

[obliviousninja]

YES, exactly this. Diagrams are soooooo helpful for me with locus q's

In terms of finding the locus of a point, let the values of the point equal x and y respectively, then eliminate parameters. In most cases its simply just completing the square and then subbing in values, from the x and the previous parts calculated ie. pq=-1

 

[hit patel]

Yes I get all that. But then when it comes to analysing the actual question, my brain freezes. I have tried my hardest to solve those question but its like my genetics just dont support parametrics. Complex Numbers is a piece of cake for me while for others its annoying. I just dont know what to do? THere is no way I am loosing my atar aim just because of parametrics in 2014.

So can someon please offer help on how to study parametrics instead of telling me answers. I had already figured out answers but its just that I need to know how to study parametrics so I become really good at it.

 

[anomalousdecay]

I have the exact same problem but with parametric loci.

I don't get it, I can do complex numbers loci questions like nothing, but for some reason with parametric loci it is just plain odd.

 

[Trebla]

Logically deduce as many results or facts (eg a point lines on this line so it should satisfy the equation when you sub it in) as you can then try it from there

 

[anomalousdecay]

I don't know. Maths in Focus does not provide good locus questions.
But I sure do know Terry Lee does for 4-unit (I've never seen his 3-unit textbook).