# Solve t for Parametric Equations: x=t^2+t, y=t^2-t

• sara_87
In summary, parametric equations are a method of representing the relationship between two variables using a third variable. To solve for t in parametric equations, the variable must be isolated on one side of the equation. The t variable serves as a parameter in these equations and allows for the representation of complex curves and shapes. Parametric equations can be graphed using specialized tools, and they have applications in various fields such as physics, engineering, economics, and biology.
sara_87

## 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

## The Attempt at a Solution

You can assume x,y are constants and find t! (Quadratic formula )

or use algebraic manipulations ... one is
x-y = 2t
once again find t

Well, adding the equations yields x+y=2t^2, whereas subtracting yields x-y=2t
See if you can use this.

## 1) What are parametric equations?

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.

## 2) How do I solve for t in parametric 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.

## 3) What is the significance of the t variable in parametric 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.

## 4) Can parametric equations be graphed?

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.

## 5) What are some real-life applications of parametric equations?

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.

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