Eliminate the parameter.
x = t^2 + 2, y = t^2 - 4
I have no clue how to do this, thanks!
Answer choices:
y = x - 6, x ≥ 1
y = x + 6, x ≥ 1
y = x2 - 6, x ≥ 1
y = x2 + 6, x ≥ 1

Question

Eliminate the parameter.
 x = t^2 + 2, y = t^2 - 4
I have no clue how to do this, thanks!
Answer choices:
y = x - 6, x ≥ 1
 y = x + 6, x ≥ 1
 y = x2 - 6, x ≥ 1
 y = x2 + 6, x ≥ 1

anonymous · Answer

since $$x=t^{2}+2 $$$$y=t^{2}-4$$ We can make t^{2} the subject which will give us$$x-2 = t^{2}$$$$y+4=t^{2}$$. Since t^{2} = t^{2}
$$x-2=y+4$$ Moving 4 to the left hand side to make y the subject will give us $$y=x-6$$, hence the first option is correct.

anonymous · Answer

BTW we eliminated t^{2} because it was the parameter we were trying to get rid of...

anonymous · Answer

thanks so much! can you check this one too, i think i figured it out...
Eliminate the parameter.
x = 7t, y = t + 4
i got...
y =  x/7+ 4  @Mousam

loser66 · Answer

yup

anonymous · Answer

yup

anonymous · Answer

well done...

anonymous · Answer

okay thank you! @Loser66  @Mousam  i have one more thats a little different and i cant quite figure it out...
Eliminate the parameter.
x = 5 cos t, y = 5 sin t

anonymous · Answer

make t the subject again

anonymous · Answer

so for x = 5cos(t), it will be t= cos^-1 (x/5)

anonymous · Answer

ok and then would y=sint would be t=sin^-1 (x/5)? @Mousam

anonymous · Answer

y=5sint*

anonymous · Answer

huh... if y=sin t then t= sin^-1 (y)

anonymous · Answer

oh

anonymous · Answer

you've written t = sin^-1 (x/5)

anonymous · Answer

it should be sin^-1 (y/5)

anonymous · Answer

you there?

anonymous · Answer

ohh! ok yeah that makes since, ok so now i have cos^-1(x/5)=sin^-1 (y/5) right? @Mousam

anonymous · Answer

yup

anonymous · Answer

but where do i go from there?

anonymous · Answer

since we know that t=cos^-1(x/5) and t=sin^1(y/5)
cos^-1(x/5) = sin^-1(y/5)
sin{cos^-1(x/5)} = y/5
5sin{cos^-1(x/5)} = y

anonymous · Answer

do you understand it?

anonymous · Answer

yes!! thanks SO much! the cos and sin were confusing me but i get it now, thanks for the help! @Mousam

anonymous · Answer

no worries... have fun and good luck

loser66 · Answer

@Mousam to me, it's x^2 + y^2 = 25

loser66 · Answer

because it forms the form of x = rcos theta, y = rsin theta.

anonymous · Answer

yea but all the examples he showed me didn't have any x^2 and y^2. i think they were just doing y=...x...

anonymous · Answer

so i just taught him that form...

anonymous · Answer

if @melper want the x^2, y^2 way then I have no problem teaching him the next time i meet him...