Eliminate the parameter to find the cartesian equation of the curve of x=t^2-3,y=t+1, for -2≤y≤4.
We want to eliminate the parameter t and find an equation in terms of x and y. From the given equations, we can solve for t in terms of y:
y = t + 1 --> t = y - 1
Substituting into the equation for x, we get:
x = t^2 - 3 --> x = (y-1)^2 - 3
Expanding and simplifying, we get:
x = y^2 - 2y - 2
Therefore, the cartesian equation of the curve is:
x = y^2 - 2y - 2, for -2 ≤ y ≤ 4.