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How to simplify this parametric?

I have the following parametric equations

[br]x = t - \dfrac{1}{t}[br]so[br]\dfrac{dx}{dt} = 1+ \dfrac{1}{t^2}[br]also[br]y= t + \dfrac{1}{t}[br]therefore[br]\dfrac{dy}{dt} = 1-\dfrac{1}{t^2}[br]

how would I find dy/dx?
I know it's dy/dt divided by dx/dt
but that would give

Unparseable latex formula:

[br]\dfrac{1-t^-^2}{1+t^-^2}[br]

and that's far too messy to be a proper equation?

TIA

(edited 10 years ago)

Reply 1

Mr M

Study Forum Helper

Think you need to check your dy/dt.

And "too messy to be a proper equation"? You what?

Reply 2

saberahmed786

Original post by Mr M

Think you need to check your dy/dt.

And "too messy to be a proper equation"? You what?

to messy when fully expressed I mean

it comes out to

[br]\dfrac{dy}{dx} = 1 - \dfrac{1}{t^2} \div 1 + \dfrac{1}{t^2}[br]

Reply 3

the bear

as Mr M says the dy/dt is wrong. your dx/dt is fine

Reply 4

0x2a

How is dy/dt = 1 - 1/t^2 ?

Reply 5

Mr M

Study Forum Helper

Original post by saberahmed786

to messy when fully expressed I mean

it comes out to

[br]\dfrac{dy}{dx} = 1 - \dfrac{1}{t^2} \div 1 + \dfrac{1}{t^2}[br]

There is no such thing as "too messy". That expression could be simplified by multiplying by

\displaystyle \frac{t^2}{t^2}

.

Don't bother doing that though as it is wrong.

Reply 6

saberahmed786

Original post by 0x2a

How is dy/dt = 1 - 1/t^2 ?

Original post by the bear

as Mr M says the dy/dt is wrong. your dx/dt is fine

Woops I forgot the t before 1/t >.<

Reply 7

Mr M

Study Forum Helper

Original post by saberahmed786

Woops I forgot the t before 1/t >.<

Ok then follow my advice in my previous post.

Reply 8

TenOfThem

Original post by saberahmed786

...

If you write

\frac{dx}{dt} = \frac{t^2+1}{t^2}

and similar for

\frac{dy}{dx}

they become far easier to divide

especially if you remember the rules for dividing fractions

Reply 9

saberahmed786

Original post by TenOfThem

If you write

\frac{dx}{dt} = \frac{t^2+1}{t^2}

and similar for

\frac{dy}{dx}

they become far easier to divide

especially if you remember the rules for dividing fractions

Original post by Mr M

Ok then follow my advice in my previous post.

I got it now, thank you :smile:

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