- #1
ttpp1124
- 110
- 4
- Homework Statement
- Determine an equation of the line of intersection of the planes 4x − 3y − z = 1 and 2x + 4y + z = 5.
Does anyone concur?
- Relevant Equations
- n/a
https://www.physicsforums.com/attachments/260155
A parametric equation is a mathematical representation of a curve or surface in terms of one or more independent variables, known as parameters. It allows us to describe the position of a point on the curve or surface in terms of the parameters.
A Cartesian equation, also known as an implicit equation, relates the dependent and independent variables using algebraic expressions. A parametric equation, on the other hand, uses parameters to describe the position of a point. This allows for more flexibility and can often simplify calculations.
Parametric equations are commonly used in physics, engineering, and computer graphics to describe the motion of objects in space. They are also used in calculus to solve problems involving curves and surfaces.
To find the parametric equation of a curve, you need to identify the independent and dependent variables and then express the dependent variable in terms of the independent variable using parameters. This can often be done by considering the properties of the curve, such as its shape and orientation.
Parametric equations allow for more flexibility in representing curves and surfaces, making them useful in a variety of fields. They also simplify calculations and can provide more insight into the behavior of a curve or surface compared to Cartesian equations.