find two sets of parametric equations for the given rectangular equation
x+y^2=4
To find two sets of parametric equations for the given rectangular equation x + y^2 = 4, we can introduce a parameter, usually denoted as t, and express x and y in terms of t.
To start, let's make y the subject of the equation. We can write y = sqrt(4 - x).
First Set of Parametric Equations:
Let's choose t = x, so our first set of parametric equations can be written as follows:
x = t
y = sqrt(4 - t)
In this case, we are letting t vary, and for each value of t, we can calculate the corresponding x and y values.
Second Set of Parametric Equations:
Alternatively, we can choose t = y to obtain the second set of parametric equations. In this case:
x = 4 - t^2
y = t
For this second set, we are letting t vary, and for each value of t, we can calculate the corresponding x and y values.
So, the two sets of parametric equations for the given rectangular equation x + y^2 = 4 are:
1st Set: x = t, y = sqrt(4 - t)
2nd Set: x = 4 - t^2, y = t