Rectangular Hyperbola (1 Viewer)

[yrtherenonames]

4 Unit exam in 14 hours...I'm gunna get nicely toasted.
Anyone got a quick proof that the foci of a rectangular hypbola xy=c^2 are
(c(rt2),c(rt2) and (-c(rt2),-c(rt2)?
Strangely, even Coroneos seems to have missed it...I think.

 

[Slidey]

The foci of a normal hyperbola are:
(+ae,0)
For rectangular, a=b, so e=sqrt2
(+sqrt(2)a,0)
Rotate this point 45 degrees to get the corrosponding focus of a rectangular hyperbola: (+sqrt(2)a+0)*(1+i)/sqrt(2)
=a(1+i)
So the focus is (a,a)
Recall a^2/2=c^2, so a=sqrt(2)c
.'. the focus is (sqrt(2)c,sqrt(2)c) #

Sorry, to clarify: to rotate 45 degrees, is to multiply by the unit vector of direction 45 degrees, that is: cis45=1/sqrt(2)+i/sqrt(2)=(1+i)/sqrt(2)

 

[shafqat]

good luck on half-yearlies
hopefully it wont be a killer like last years

 

[yrtherenonames]

Cheers, I'm sure they won't ask it, but good to know
Shafqat its hard to tell because we did conics instead of circular motion at this time of year, but your paper looked a bit tough.

 

[Slidey]

Oh, BTW, while this method is completely valid, you should perhaps look up the other method of finding the focus, as that doesn't use complex numbers. I believe it uses pythagoras.

 

[shafqat]

Cheers, I'm sure they won't ask it, but good to know
Shafqat its hard to tell because we did conics instead of circular motion at this time of year, but your paper looked a bit tough.

really? that's interesting. i thought conics was a bit rushed last year, but i reckon its easier than circular motion, so i don't know about the swap.

 

[dawso]

am i reading correctly that ur skool (syd grammar??) did circular motion at this time last year??

 

[shafqat]

if my memory serves me correctly we had done integration, complex, motion and polynomials.

 

[~ ReNcH ~]

if my memory serves me correctly we had done integration, complex, motion and polynomials.

I was always under the impression that most schools left Mechanics until last, seeing as it's probably the hardest MX2 topic.

 

[shafqat]

I agree it is a hard topic, so I would much prefer it to be taught earlier. And yes, looking at other schools' trial papers, most schools leave motion until the end.