- #1
sara_87
- 763
- 0
Homework Statement
i want to make t the subject of any of the following equations inorder to find the cartesion equation. any ideas?:
x=t^2+t
y=t^2-t
Parametric equations are a way to represent the relationship between two variables, typically x and y, in terms of a third variable, usually denoted as t. This allows for the depiction of curves and shapes that may not be easily expressed using traditional algebraic equations.
To solve for t in parametric equations, you first need to isolate the variable t on one side of the equation. In the given example, we can rewrite the equations as t=x/(1+t) and t=(y+1)/x. Then, by setting these two equations equal to each other and solving for t, we can find the value of t that satisfies both equations.
The t variable in parametric equations serves as a parameter or independent variable that determines the values of x and y. It allows for the representation of curves and shapes that cannot be easily expressed using traditional equations.
Yes, parametric equations can be graphed using a parametric plotter or graphing calculator. By plotting the values of x and y for different values of t, a curve or shape can be generated.
Parametric equations are commonly used in physics, engineering, and computer graphics to model and analyze motion and trajectories. They are also used in economics and finance to represent relationships between variables and in biology to model growth and population dynamics.