The method of expressing a curve using a parameter t, such as x = f(t) and y = g(t), is called a parametric representation.
Example ① Eliminate t from x = t+1 and y = t²−1.
Solution: Substitute t = x−1 → y = (x−1)² − 1 (a parabola)
Solution: Substitute t = x−1 → y = (x−1)² − 1 (a parabola)
Key Point
- Eliminating the parameter returns the equation to its ordinary form.
Practice Problems
- Eliminate t from x=2t and y=t²+1.
Solutions and Explanations
- Solution: y = x²/4 + 1