Home

Parametric Equation of Line Calculator

Online parametric line: enter a point, direction vector and parameter t to find the coordinates.

展开更多 ▾
x=x₀+at, y=y₀+bt
Point
x
y
Direction
x
y
Any sign

📖 Tutorial | Parametric Line

1. Definition
A line through P₀(x₀,y₀) with direction (a,b) has x=x₀+at, y=y₀+bt.
2. Formula & Notation
Point, direction(a,b)
3. Properties & Laws
  • Parametric form;
  • t proportional to directed distance;
  • Eliminate t for the ordinary equation;
  • (a,b)≠(0,0).
4. Steps
  1. Enter point, direction, t;
  2. Click "Point";
  3. Or click "Load Example".
5. Worked Examples
Example: (1,2), direction (3,4), t=2: (7,10).
6. Common Pitfalls
Non-zero direction;
t any sign;
Mind a or b zero when eliminating.

❓ FAQ | Parametric Line

Parametric?
x,y in t.
Direction?
(a,b).
t?
Distance ratio.
Eliminate?
Substitute back.
Example?
(7,10).
Benefit?
Motion.