Explicit form to parametric form

In summary, the conversation discusses how to convert a plane from explicit form to parametric form. The process involves using two parameters and there may be multiple ways to parameterize a geometric object.
  • #1
ydan87
25
0
Hi there,
I have the plane in an explicit form:
12x + 2y – 20z = -56

How do I make it in parametric form?

Thanks in advance
 
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  • #2
Take for example the example of:

y=x^2

It can be parametrized by using a free parameter t as:

x=t and y=t^2 Hope I've helped you a bit.
 
  • #3
A plane is two-dimensional so parametric equations will require two parameters. You can use any two of x, y, and z as as those parameters.

It might help you to remember that there is no "unique" parameterization for a geometric object. There may be many different ways to parameterize such a figure.
 

Related to Explicit form to parametric form

What is the difference between explicit form and parametric form?

The explicit form of a equation is when the variables are expressed in terms of one another, such as y = mx + b. The parametric form, on the other hand, represents the variables as separate functions of a parameter, usually denoted by t.

When is it more appropriate to use explicit form over parametric form?

Explicit form is typically used when the relationship between the variables is clear and easy to express in terms of one another. Parametric form is useful when the relationship is more complex and needs to be broken down into separate functions.

How do you convert from explicit form to parametric form?

To convert from explicit form to parametric form, you need to solve for one variable in terms of the other, and then express both variables as separate functions of a parameter. For example, in the equation y = mx + b, you can solve for x as x = (y-b)/m, and then express both x and y as functions of t, such as x(t) and y(t).

What are the advantages of using parametric form?

Parametric form allows for more flexibility in representing complex relationships between variables. It also allows for the use of trigonometric functions to represent curves and other geometric shapes, making it useful in fields such as physics and engineering.

Can you convert from parametric form back to explicit form?

Yes, it is possible to convert from parametric form back to explicit form by eliminating the parameter t and solving for one variable in terms of the other. However, this process can be more complex and may result in multiple solutions or the need for approximations.

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