How the Parametric Equation Calculator Works
The Parametric Equation Calculator converts linear parametric equations into Cartesian form. Parametric equations describe x and y using a shared parameter, usually t.
A linear parametric curve has the form:
To eliminate the parameter, solve x(t) for t and substitute into y(t).
Parametric to Cartesian Formula
If:
then:
Substitute that into:
giving:
How to Use the Calculator
- Enter x(t) as a linear expression in t.
- Enter y(t) as a linear expression in t.
- Click Convert to Cartesian Form.
- Review the solved expression for t and the final Cartesian form.
Input Examples
| Expression | Accepted input |
|---|---|
| 2t + 1 | 2*t + 1 |
| -3t + 5 | -3*t + 5 |
| t - 4 | t - 4 |
| 7 | 7 |
Worked Example
Given:
x(t) = 2t + 1 y(t) = 3t + 4
Solve x(t) for t:
x = 2t + 1 x - 1 = 2t t = (x - 1) / 2
Substitute into y(t):
y = 3((x - 1) / 2) + 4 y = (3x + 5) / 2
Limitations
x = cos(t), y = sin(t) may not have a single Cartesian form y = f(x).
Frequently Asked Questions
What are parametric equations?
Parametric equations express coordinates using a shared parameter, usually t. For example, x(t) and y(t) together define a curve.
How do you eliminate the parameter?
Solve one equation for t, then substitute that expression into the other equation.
Can every parametric equation become y = f(x)?
No. Some curves cannot be represented as a single function y = f(x), especially circles and curves that loop back.
What happens if x(t) is constant?
If x(t) is constant, the Cartesian result is a vertical line, such as x = 5, not a function y = f(x).