Answer:
Eliminating the parameter, the equation is ![y = x - 2](https://tex.z-dn.net/?f=y%20%3D%20x%20-%202)
Step-by-step explanation:
We are given the following parametric equations:
![x = t^2 + 1](https://tex.z-dn.net/?f=x%20%3D%20t%5E2%20%2B%201)
![y = t^2 - 1](https://tex.z-dn.net/?f=y%20%3D%20t%5E2%20-%201)
We want to eliminate the parameter t. From the first equation:
![x = t^2 + 1](https://tex.z-dn.net/?f=x%20%3D%20t%5E2%20%2B%201)
![t^2 = x - 1](https://tex.z-dn.net/?f=t%5E2%20%3D%20x%20-%201)
Replacing in the second equation:
![y = x - 1 - 1](https://tex.z-dn.net/?f=y%20%3D%20x%20-%201%20-%201)
![y = x - 2](https://tex.z-dn.net/?f=y%20%3D%20x%20-%202)
Eliminating the parameter, the equation is ![y = x - 2](https://tex.z-dn.net/?f=y%20%3D%20x%20-%202)