How do you turn these parametric equations into a Cartesian equation

[midnight geode]

Im not sure how to solve this problem... tried making 't' the subject but i dont think thats the right way for this type of question

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[gaunt wave]

try squaring both equations and work from there

[midnight geode]

I did that and idk what happened after 😭

Wait maybe I’ll retry that

Yeah idk

What to do

[still cliff]

$$y= \frac{1-t^2}{1+t^2}$$
can be rewritten as
$$y= \frac{(1-t)(1+t)}{(1+t)(1+t)}$$
$$y=\frac{1-t}{1+t}$$

[viral yew]

π

[still cliff]

now subject t in terms of y

so that you can plug it into the first equation to eliminate t

whats the final ans given as?

[midnight geode]

How did u get from step 1 to step 2

I know how you got the numerator, by difference of 2 squares, but I’m confused on how you factorised denominator

[still cliff]

ohh my bad lol made a mistake

you can try making t^2 the subject here

for the 2nd equation

$$y(1+t^2)=(1-t^2)$$
$$y+yt^2=1-t^2$$
$$yt^2+t^2=1-y$$
$$t^2(y+1)=1-y$$
$$t^2=\frac{1-y}{y+1}$$

[viral yew]

π

[still cliff]

now subject t and t^2 into the first equation

and simplify

[midnight geode]

I think I made it more confusing lol

I got a cubic equation but haven’t finished it yet

[still cliff]

huh

can u send ur working

[midnight geode]

But according to the answers, the Cartesian equation is x^2 + y^ 2 = 1

[still cliff]

yes I simplified it and got it asw

[still cliff]

you might hv made an error

[gaunt wave]

note that (1+t^2)^2 = 1 + 2t^2 + t^4

(1-t^2)^2 = 1 - 2t^2 + t^4

[gaunt wave]

can you somehow get from this to the statement above

[still cliff]

It would be better if you simplified this instead of bringing the denominator to the top

[still cliff]

Since you got it to this point now square both sides

And you will be able to cancel the y+1 on the numerator

[midnight geode]

Oh my gosh it works

Thanks so much 🙏

[gaunt wave]

a shorter approach is to square both sides

[still cliff]

yw

[gaunt wave]

then add them together, noticing the perfect square and simplifying the fraction to 1

[midnight geode]

+close

[lunar cosmos]

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[lunar cosmos]

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