Do you memorise or derive formulas? (1 Viewer)

[danz90]

Like, in particular... do you guys actually memorise the equations for chords/tangents etc etc in the parabole chapter?

I usually just derive most of them while answering question.

But then there are trig formulas and rules that you just have 2 remember.

 

[QuLiT]

i derive what i can but sometimes you have to remember

 

[Justina]

I memorise - but end up forgetting at least one per test -.-
And i'm pretty much screwed if they ask to derive them.....

 

[henry08]

I memorise. I'm screwed mostly for deriving.

 

[tommykins]

回复: Re: Do you memorise or derive formulas?

i always derive. bar the double angle + trig identities.

 

[dolbinau]

Re: 回复: Re: Do you memorise or derive formulas?

Are these the Locus questions? I derive. Sometimes they ask you to 'show the equation of the tangent is' something; how can you do that if you just write down the formula you memorised? (Which would be the same as what they've given you )

 

[I-Love-Jesus]

Re: 回复: Re: Do you memorise or derive formulas?

i always derive. bar the double angle + trig identities.

I would say this ^
Except know them well enough that you'd be able recognise if you've made a mistake in your derivation. I guess be able to recognise them without having memorised them. 90% of the time in locus and parabola questions they will ask you to derive anyway.

 

[Aznmichael92]

i try to remember formulas backwards. It is not easier to remember but once you remember it, you most likely wont forget it.

so instead of remembering cos^2 + sin^2 = 1, i remember 1 = cos^2 + sin^2

hope you guys got what I was saying

 

[QuLiT]

you have to derive everything other than the chord of contact and pq= -1 for a latus rectum

 

[QuLiT]

yes that's chord of contact. right?!

 

[dolbinau]

I have the locus chapter. Is there a way I can derive the chord of contact then, so I understand it?

Also in some questions we often have to find pq= something but it's not always -1. What are these cases?

 

[u-borat]

err pq is only -1 when its a focal chord.
its more likely not -1 than it is.

chord of contact is easy to derive.

take external point x0,y0.
this point satistifes both tangent equations. (cant remember tangent equation off top of head)

then you say that only one line goes through both points, and that line is chord of contact.

 

[QuLiT]

ahh yes forgot that its focal chord for pq=-1 not latus rectum

 

[dolbinau]

So It's just the tangent/normal equations with x0, y0 instead of 2ap and 2aq?

Well, thanks.

 

[u-borat]

sorry i'll make it clearer.

tangent equals

xx1=2a(y+y1)

at (x1, y1)

tangent equals

xx2=2a(y+y2)

at x2,y2

therefore let the point of contact of these two tangents be x0,y0

now

x0,y0 satisfies BOTH xx1=2a(y+y1) AND xx2=2a(y+y2)

therefore, both x1,y1 and x2,y2 satisfy the generic line:

xx0=2a(y+y0)

but: only one line satisfies both x1,y1 and x2,y2 and that is the chord of contact.

therefore xx0=2a(y+y0) is the chord of cotnact.

 

[dolbinau]

Thanks, I get that proof now. And I know I sound like a lost cause but where does x(x1)=2a(y+y1) come from?

 

[Caitlin63]

Its the equation of the tangent at the point (x1,y1)

 

[dolbinau]

Ok, thanks!