How would I convert cartesian equation to parametric?
For example: 2x-y+3z-6=0
To convert a Cartesian equation to a parametric equation, you need to express each variable (x, y, and z) in terms of a parameter (usually represented by a letter, such as t). Here's how you can convert the given equation, 2x - y + 3z - 6 = 0, into parametric form:
Step 1: Solve for one variable (preferably x, y, or z) in terms of the remaining variables.
Let's solve for x:
2x - y + 3z - 6 = 0
2x = y - 3z + 6
x = (y - 3z + 6) / 2
Step 2: Choose two of the remaining variables (y and z in this case) and express them in terms of a parameter (t).
Let's choose y and z:
y = t
z = s (you can use a different letter as the parameter)
Step 3: Substitute the parameter expressions into the equation for x.
x = (y - 3z + 6) / 2
x = (t - 3s + 6) / 2
So, the parametric equations for the given Cartesian equation are:
x = (t - 3s + 6) / 2
y = t
z = s
These parametric equations represent a parameterized representation of the original cartesian equation. They allow you to express points on the surface defined by the equation in terms of the parameters t and s. By choosing different values for t and s, you can generate various points on the surface.