find two sets of parametric equations for the given rectangular equation
x+y^2=4
can you check my work?
x=-y^2+4
y=-t^2
x=-t^2+4
x=-t^3
y=-t^3+4
To find parametric equations for the given rectangular equation x + y^2 = 4, follow these steps:
1. Solve the equation for x:
x = 4 - y^2
2. Choose a parameter (let's use t) and express y in terms of t:
y = t
3. Substitute the value of y into the equation for x:
x = 4 - (t^2)
Therefore, one set of parametric equations for the rectangular equation x + y^2 = 4 is:
x = 4 - t^2
y = t
Regarding your attempt, your second set of parametric equations (x = -t^3, y = -t^3 + 4) is incorrect. It does not satisfy the original equation x + y^2 = 4.