Author Topic: Locus and parabola (Read 6569 times) Tweet Share

vyca · « **on:** September 18, 2016, 12:08:22 pm »

So I have no idea/don't remember anything about this prelim topic and it keeps popping up in hsc past papers....how should I approach studying it? Should I go back and re-do and re-learn the entire chapter

RuiAce · « **Reply #1 on:** September 18, 2016, 12:25:11 pm »

What is confusing you in particular?

lozil · « **Reply #2 on:** September 19, 2016, 09:46:06 pm »

I always have this problem too... I think I've revised locus but then I get a question and have no idea how to answer it $:-\$

RuiAce · « **Reply #3 on:** September 19, 2016, 09:51:30 pm »

Quote from: lozil on September 19, 2016, 09:46:06 pm

I always have this problem too... I think I've revised locus but then I get a question and have no idea how to answer it $:-\$

Well there comes a requirement to break down the question and try to draw out what's relevant at the time.

Let's try an example question. Provide one.

lozil · « **Reply #4 on:** September 19, 2016, 09:59:00 pm »

Quote from: RuiAce on September 19, 2016, 09:51:30 pm

Well there comes a requirement to break down the question and try to draw out what's relevant at the time.

Let's try an example question. Provide one.

I guess it just varies with the question... like I always get confused with competing the square ones (e.g. find the focus of X^2 + 6x - 12y - 3 = 0). I know how to do them, I just get confused with all the numbers under exam conditions

lozil · « **Reply #5 on:** September 19, 2016, 10:05:23 pm »

Quote from: RuiAce on September 19, 2016, 09:51:30 pm

Well there comes a requirement to break down the question and try to draw out what's relevant at the time.

Let's try an example question. Provide one.

And questions like "Point P moves so that PA^2 + PB^2 = 4 where A = (3,-1) and B = (-5,4). Find the equation of the locus of P."

RuiAce · « **Reply #6 on:** September 19, 2016, 10:05:44 pm »

Quote from: lozil on September 19, 2016, 09:59:00 pm

I guess it just varies with the question... like I always get confused with competing the square ones (e.g. find the focus of X^2 + 6x - 12y - 3 = 0). I know how to do them, I just get confused with all the numbers under exam conditions

$\text{You want your equation to ALWAYS be in this form or similar}\\ (x-h)^2=4a(y-k)\\ \text{Whenever this does not occur, complete the square.}\\ \text{Memorise methods such as these and figure out why they work.}$
$\begin{align*}x^2+6x-12y-3&=0\\ x^2+6x+9&=12y+12\\ (x+3)^2&=12(y+1)\end{align*}$
$\text{Then, it's just a matter of knowing your formulas.}$

RuiAce · « **Reply #7 on:** September 19, 2016, 10:09:11 pm »

Quote from: lozil on September 19, 2016, 10:05:23 pm

And questions like "Point P moves so that PA^2 + PB^2 = 4 where A = (3,-1) and B = (-5,4). Find the equation of the locus of P."

$\text{Instead of overanalysing question types like this}\\ \text{Just know the METHOD. Memorise the METHOD.}\\ \text{It should not be that obvious to a 2U student that this is an circle.}$
$\text{Write out the distances given}\\ \textit{Let }P\text{ be the point }(x,y) \\ \begin{align*}PA^2&=(x-3)^2+(y+1)^2\\ PB^2&=(x+5)^2+(y-4)^2\end{align*}\\ \text{Expand and THEN do battle with algebra.}$
$\text{Unless your memory is good enough to memorise the obvious}\\ \text{You generally don't have a direction to head for these questions.}$

lozil · « **Reply #8 on:** September 19, 2016, 10:14:06 pm »

Quote from: RuiAce on September 19, 2016, 10:09:11 pm

$\text{Instead of overanalysing question types like this}\\ \text{Just know the METHOD. Memorise the METHOD.}\\ \text{It should not be that obvious to a 2U student that this is an circle.}$
$\text{Write out the distances given}\\ \textit{Let }P\text{ be the point }(x,y) \\ \begin{align*}PA^2&=(x-3)^2+(y+1)^2\\ PB^2&=(x+5)^2+(y-4)^2\end{align*}\\ \text{Expand and THEN do battle with algebra.}$
$\text{Unless your memory is good enough to memorise the obvious}\\ \text{You generally don't have a direction to head for these questions.}$

Ok thanks. I guess I've just got to do lots of practice (especially under exam conditions!) Can't believe HSC is only 3 weeks away

jamonwindeyer · « **Reply #9 on:** September 19, 2016, 10:59:35 pm »

Quote from: lozil on September 19, 2016, 10:14:06 pm

Ok thanks. I guess I've just got to do lots of practice (especially under exam conditions!) Can't believe HSC is only 3 weeks away

We're here to help you every step of the way!!

vyca · « **Reply #10 on:** September 26, 2016, 12:47:45 pm »

Should I be memorising all the different formula's and knowing letter is the vertex, directrix etc.?

RuiAce · « **Reply #11 on:** September 26, 2016, 01:19:16 pm »

Quote from: vyca on September 26, 2016, 12:47:45 pm

Should I be memorising all the different formula's and knowing letter is the vertex, directrix etc.?

After you work through the PS=PM derivation, yes. And they are mentioned on your reference sheet.

You should try to figure out why the formulae are true as well.

vyca · « **Reply #12 on:** September 26, 2016, 01:51:29 pm »

Quote from: RuiAce on September 26, 2016, 01:19:16 pm

After you work through the PS=PM derivation, yes. And they are mentioned on your reference sheet.

You should try to figure out why the formulae are true as well.

Is that all there is to Parabola & locus, the PS=PM derivation and the formula's?

RuiAce · « **Reply #13 on:** September 26, 2016, 02:00:35 pm »

Quote from: vyca on September 26, 2016, 01:51:29 pm

Is that all there is to Parabola & locus, the PS=PM derivation and the formula's?

PS=PM isn't restricted to the parabola - it can be the circle or a straight line as well. But yes that's basically it to the topic.

vyca · « **Reply #14 on:** September 26, 2016, 03:41:35 pm »

Quote from: RuiAce on September 26, 2016, 02:00:35 pm

PS=PM isn't restricted to the parabola - it can be the circle or a straight line as well. But yes that's basically it to the topic.

Thankyou RuiAce for your help!

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Author Topic: Locus and parabola (Read 6569 times) Tweet Share

vyca

Locus and parabola

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