Question

A curve in R^3 (set of real numbers) is generated by the intersection of the elliptic cylinder (x^2/2^2) + (y^2/3^2) = 1 and the PLANE z= (sq.rt(5)/2)x.
a) Find the parametric representation for the curve with respect to a parameter t.
b) Find the length of the curve from t=0 to t=pi/2.

Answer 1

a) I'm not sure if this is the right way, but can't you say x = t and make your y(x) an y(x(t)) ? So this would mean that\[y(x(t)) = \sqrt{2^2+3^2-3^2t^2} / 2\]

Answer 2

okay!! go on!

Answer 3

that isnt parametricising the equation

Answer 4

thats what i thought! i had to do something like.. x=cos t , y=sin t and something like that

Answer 5

x = a cos(t)
y = b sin(t)

when x = 0; y = 3 which leads us to b=3
when y = 0; x = 2 which leads to a=2

x = 2 cos(t)
y = 3 sin(t)

z = (sqrt(5)/2) x
z = (sqrt(5)/2) 2 cos(t)

z = sqrt(5) cos(t)

Answer 6

yes.. i got that far... but i am stuck there

Answer 7

\[\int_{0}^{pi/2}\sqrt{[x'(t)]^2+[y'(t)]^2+[z'(t)]^2}\ dt\]

Answer 8

yes... keep going please!

Answer 9

trying to see if im missing any parts to it :) its been awhile since i tried these

Answer 10

i am missing a part, just cant quite see how it fits in yet

Answer 11

\[\int_{a}^{b}\ f\left(x(t),y(t),z(t)\right)\ \sqrt{[x'(t)]^2+[y'(t)]^2+[z'(t)]^2}\ dt\]

Answer 12

its what to do with the f(.......) part i cant quite determine

Answer 13

got it ...lol

Answer 14

f(x,y,z) = \(\frac{x^2}{4} + \frac{y^2}{9} = 1\)

Answer 15

well, its something to do with that

Answer 16

oh.. okay...

Answer 17

is there more to it or does it end there?

Answer 18

there is more to it, but I cant focus at the moment, got my international business class soming up in a few

Answer 19

oh.. okay... can you help me out when you can witht he same problem!

Answer 20

just another question i am finding it difficult to figure out

http://openstudy.com/groups/mathematics#/users/benfraser1012