Thread: more parametric equations Part 1

1. more parametric equations Part 1

Eliminate the parameter, t to obtain the cartesian equation in x and y. Sketch the curve, taking note of any restrictions

a) $\displaystyle x = 2at, ~ y = at^2$

b) $\displaystyle x = V t \cos a, ~ y = V t \sin a - \frac{g}{2} t^2$ where V, g and a are constants

c) $\displaystyle x = t + \frac{1}{t}, ~ y = t^2 + \frac{1}{t^2}$

I know it's a lot and i really dont expect this all to be answered, i just put all the questions which i had serious trouble with and i would be SO grateful to anyone who could give me a few pointers on how to solve these because i just dont know how to get rid of the t OR find the restrictions. again , i know there are alot of questions and im not just expecting answers or a cheap way to get answers for hw, i realli just dont understand it and would seriously appreciate any help .
thankyou guyz !

2. Originally Posted by THSKluv
Eliminate the parameter, t to obtain the cartesian equation in x and y. Sketch the curve, taking note of any restrictions

a) $\displaystyle x = 2at, ~ y = at^2$

b) $\displaystyle x = V t \cos a, ~ y = V t \sin a - \frac{g}{2} t^2$ where V, g and a are constants

c) $\displaystyle x = t + \frac{1}{t}, ~ y = t^2 + \frac{1}{t^2}$

I know it's a lot and i really dont expect this all to be answered, i just put all the questions which i had serious trouble with and i would be SO grateful to anyone who could give me a few pointers on how to solve these because i just dont know how to get rid of the t OR find the restrictions. again , i know there are alot of questions and im not just expecting answers or a cheap way to get answers for hw, i realli just dont understand it and would seriously appreciate any help .
thankyou guyz !
a) $\displaystyle x = 2at \Rightarrow t = \frac{x}{2a}$. Substitute this into $\displaystyle y = at^2$.

b) Similar to a).

c) $\displaystyle x = t + \frac{1}{t} \Rightarrow x^2 = t^2 + 2 + \frac{1}{t^2}$. Now substitute $\displaystyle y = t^2 + \frac{1}{t^2}$.