Question

Can all parametric equations be written in Cartesian form?

Answer 1

for example:

can x=t^(3) and y=t^(2)+t be written in cartesian form?

Answer 2

\[x=t^{3}\]
\[y=t ^{2}+t\]

Answer 3

yh, I suppose you'ld have to differentiate find dy/dx = (dx/dt)*(dt/dy)

Answer 4

you sure?
Do you mean differentiate them both, combine the differentials and then integrate to form 1 equation?

Answer 5

\[dy/dx = (dx/dt)*(dt/dy)\] to find the gradient

Answer 6

I know that, but what has that got to do with parmetric equation conversion?

Answer 7

i dont want to find any gradients

Answer 8

by cartesian form what do you mean exactly, what kind of expression would like to see for example, in the equations above
\[dy/dx = (dx/dt)/(dt/dy)= 2t ^{2}/2t+1\]

Answer 9

I would like to see a single equation in terms of ys and xs only

Answer 10

or substitute t
\[x=t^{3} \therefore t = \sqrt[3]{x} \]
\[y=t^{2} +t \therefore y=(\sqrt[3]{x})^{2} +(\sqrt[3]{x}) \]
\[y =(x ^{2}+x)^{1/3}\]

Answer 11

I know how to do it, but can ALL parametric equations be put into cartesian?

Answer 12

nice q tho, prolly as long as both x and y terms relate with each other