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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: un on November 15, 2007, 07:41:45 pm

Title: Cartesion Equation/Parametrics ----HELP Needed?!?!?!?
Post by: un on November 15, 2007, 07:41:45 pm
The position vector of a particle at any time t is given by the equation:

r(t)= (2cos(t)+3)i +(3sin(t)+5)j

Find the Cartesian Equation of the path of the particle.

Thanks Guys
Title: Cartesion Equation/Parametrics ----HELP Needed?!?!?!?
Post by: cara.mel on November 15, 2007, 07:55:15 pm
x = 2 cos t + 3
y = 3 sin t + 5

Equation that links them together:
sin^2 t + cos^2 t = 1

cos t = (x-3)/2
sin t = (y-5)/3

=> ((x-3)/2)^2 + ((y-5)/3)^2 = 1
(x-3)^2/4 + (y-5)^2/9 = 1
Title: Re: Cartesion Equation/Parametrics ----HELP Needed?!?!?!?
Post by: Collin Li on November 15, 2007, 07:55:19 pm
Quote from: "un"
The position vector of a particle at any time t is given by the equation:

r(t)= (2cos(t)+3)i +(3sin(t)+5)j

Find the Cartesian Equation of the path of the particle.

Thanks Guys


x = 2cost + 3 => (x-3)/2 = cost
y = 3sint + 5 => (y-5)/3 = sint

sin^2[t] + cos^2[t] = 1
=> (x-3)^2/4 + (y-5)^2/9 = 1
Title: Cartesion Equation/Parametrics ----HELP Needed?!?!?!?
Post by: Collin Li on November 15, 2007, 07:55:43 pm
Ouch, I don't know how close that was...
Title: Cartesion Equation/Parametrics ----HELP Needed?!?!?!?
Post by: cara.mel on November 15, 2007, 08:01:50 pm
It was within a few seconds I think