Conics Question - Ellipse. (1 Viewer)

[Gussy Booo]

In the general formula of a ellipse, WHY does b^2=a^2(1-e^2) ?

Thanks in advanced.

 

[gurmies]

In the general formula of a ellipse, WHY does b^2=a^2(1-e^2) ?

Thanks in advanced.

This is because when you derive the formula of an ellipse, you end up with x^2/a^2 + y^2/a^2(1-e^2) = 1. We let b^2 = a^2(1-e^2) to make things neater and simpler, I think.

 

[Gussy Booo]

This is because when you derive the formula of an ellipse, you end up with x^2/a^2 + y^2/a^2(1-e^2) = 1. We let b^2 = a^2(1-e^2) to make things neater and simpler, I think.

I understand where it comes from, but I do not know WHY.

"To make things neater and simpler" does not leave me satisfied.

Helphelp.

 

[gurmies]

I understand where it comes from, but I do not know WHY.

"To make things neater and simpler" does not leave me satisfied.

Helphelp.

Ellipse/Proofs - Wikipedia, the free encyclopedia

This should help.

 

[Gussy Booo]

Ellipse/Proofs - Wikipedia, the free encyclopedia

This should help.

Thank you.

 

[Jacob1991]

This is because when you derive the formula of an ellipse, you end up with x^2/a^2 + y^2/a^2(1-e^2) = 1. We let b^2 = a^2(1-e^2) to make things neater and simpler, I think.

yep, using b^2 = a^2(1-e^2) has absolutely no other purpose except to make the working a bit neater.

 

[tommykins]

kinda like why we use i instead of sqrt(-1)

 

[Schoey93]

I thought that you couldn't have the square root of a negative number... is that just a (false) concept?

 

[tommykins]

for a mathematics lover who refuses to do high school math, you sure know your math.

but yes you can have sqrt of a negative number

 

[addikaye03]

I thought that you couldn't have the square root of a negative number... is that just a (false) concept?

i don't know if this is serious or not, it's a true concept.

We let i=rt(-1) [such that i^2=-1], which is called an 'imaginary number'. Sometimes numbers have both real and imaginary components, these are called 'Complex numbers'. They are in the form z=x+iy. It's a concept dealt that's dealt with in 4U maths.

 

[study-freak]

i don't know if this is serious or not, it's a true concept.

We let i=rt(-1) [such that i^2=-1], which is called an 'imaginary number'. Sometimes numbers have both real and imaginary components, these are called 'Complex numbers'. They are in the form z=x+iy. It's a concept dealt that's dealt with in 4U maths.

No, this is incorrect.
Complex numbers do not need to have both real and imaginary parts.
E.g. real number system belongs to complex number system.

A number that has both of those parts is a non-real complex number that is not purely imaginary.

 

[addikaye03]

No, this is incorrect.
Complex numbers do not need to have both real and imaginary parts.
E.g. real number system belongs to complex number system.

A number that has both of those parts is a non-real complex number that is not purely imaginary.

yeah, i know, i was just trying to give the kid a quick idea, didn't want to go into details about systems etc

 

[study-freak]

yeah, i know, i was just trying to give the kid a quick idea, didn't want to go into details about systems etc

Hmm, ok.

 

[addikaye03]

Hmm, ok.

The kid thought that rt(-1) was a "false concept" lol, i wasn't going to start on about how x,y E R but R is a set of C etc, wasn't required.

 

[study-freak]

The kid thought that rt(-1) was a "false concept" lol, i wasn't going to start on about how x,y E R but R is a set of C etc, wasn't required.

Yea, I understand.
I said "ok" as in I got what you meant.

 

[addikaye03]

Yea, I understand.
I said "ok" as in I got what you meant.

Ahh ok man lol Goodluck with marks btw, as you saw on my 99.95 list, i expect big things lol

 

[study-freak]

Ahh ok man lol Goodluck with marks btw, as you saw on my 99.95 list, i expect big things lol

Haha, thanks
But I am pretty sure that 99.95 wouldn't be for me

 

[addikaye03]

Haha, thanks
But I am pretty sure that 99.95 wouldn't be for me

Well, i suppose i'm only judging off your maths. Since i read you think 83/84 in MX1 and about 110 in MX2, i mean thats 100 or 99 in Mx1 and 98 (high end)-99 in MX2. How do you think you went at your other subkjects?

I think i got 78/84 in MX1 (just one mark stuff dropped here and there) and 106/120 in MX2 (same, and couldn't get the probability in Q8 out)...

 

[study-freak]

Well, i suppose i'm only judging off your maths. Since i read you think 83/84 in MX1 and about 110 in MX2, i mean thats 100 or 99 in Mx1 and 98 (high end)-99 in MX2. How do you think you went at your other subkjects?

I think i got 78/84 in MX1 (just one mark stuff dropped here and there) and 106/120 in MX2 (same, and couldn't get the probability in Q8 out)...

For now, 83 in MX1 seems right, but it doesn't mean that I will get 83 because I could have missed something.
I can't remember everything I wrote so yea.

And MX2 was counting assuming no stupid mistakes
I realistically look at ~105-107 as I skim read Terry Lee's solutions for 4u.
and yea lol, I hated the paper.

And yea, in other subjects
ESL: terrible module B, but it shouldn't be that bad when everything is added up.
I reckon I might get about 92/100 overall, because I got that in my trials.

Physics: I don't have problems with calculations but like... MC-2 mistakes
Option (astrophysics)-prob 2 or, if I face bad luck, some more marks off because I couldn't reason why adaptive optics wasn't suited to radio telescopes properly and I wasn't too sure about the movement of the spectroscopic binary system in one of the questions.
so max:96/100

Chem: Shipwrecks-I think I might get 2 marks off from Al, Cu guttering? question because I didn't talk about Al's passivating barrier
MC-I'm not quite sure about pH adjustiment one because textbooks give different opinions (I followed conquering chem)
max:97-98/100

 

[addikaye03]

For now, 83 in MX1 seems right, but it doesn't mean that I will get 83 because I could have missed something.
I can't remember everything I wrote so yea.

And MX2 was counting assuming no stupid mistakes
I realistically look at ~105-107 as I skim read Terry Lee's solutions for 4u.
and yea lol, I hated the paper.

And yea, in other subjects
ESL: terrible module B, but it shouldn't be that bad when everything is added up.
I reckon I might get about 92/100 overall, because I got that in my trials.

Physics: I don't have problems with calculations but like... MC-2 mistakes
Option (astrophysics)-prob 2 or, if I face bad luck, some more marks off because I couldn't reason why adaptive optics wasn't suited to radio telescopes properly and I wasn't too sure about the movement of the spectroscopic binary system in one of the questions.
so max:96/100

Chem: Shipwrecks-I think I might get 2 marks off from Al, Cu guttering? question because I didn't talk about Al's passivating barrier
MC-I'm not quite sure about pH adjustiment one because textbooks give different opinions (I followed conquering chem)
max:97-98/100

Say you get:
MX2: 98
MX1: 99
ESL: 92
Physics: 95
Chemistry: 97

Gee that's gotta be close to 99.95 bro

+ I didn't really love the Mx2 paper either, i don't like when they spread the difficulty throughout the paper, like q8, apart from probability Q was simple. I prefer when papers get gradually harder and harder