Question

eliminate the parameter
x=t^2+2, y=t^2-4
please explain the steps

Answer 1

you can start by isolating the t^2, and plug in the other equation

Answer 2

so... step 1: isolating the t^2 from either equation. I picked the second.
you should get t^2 = y+4

Answer 3

step 2: plug that in the first
x = t^2 + 2
x = (y + 4) + 2

Answer 4

there's your answer, and you can try to simplify to make it nice :)

Answer 5

I was thinking to just simply write the expression for x - y

x - y = (t^2 + 2) - (t^2 - 4)
= t^2 - t^2 + 6
= 6
So
x - y = 6

Answer 6

@Hero That works too :). It just depends on the problem I guess

Answer 7

There are answer choices to this practice problem, and @alias I used the problem x=t^2+2 and I got x-2=t^2 thus, y=x-2-4 and y=x-6 and that is one of the answer choices which is y=x-6, x> or equal to 1. Is this right? what does the greater than or equal to sign have to do with this problem?

Answer 8

y=x-6 is right. And what's going on with the x> or equal to 1? Can you elaborate?

Answer 9

Ohhh wait nevermind I answered my own question haahahah thank you! Can you help me with another problem? @alias

Answer 10

lol, sure :)

Answer 11

x= sqrt t , y=2t+5
How do I deal with the sqrt? @alias

Answer 12

solve for t, then plug in the other one

Answer 13

same procedure

Answer 14

What happens if you take \(x = \sqrt{t}\) and then square both sides?

Answer 15

the sqrt goes away? @Hero

Answer 16

Yes and then you'd have \(x^2 = t\)

Answer 17

From there, you could easily substitute for t in the second equation.

Answer 18

Would the answer be y=2x^2+5? @Hero

Answer 19

That's how I was imagining it.

Answer 20

Yes! Thank you :D @Hero