Eliminate the parameter to find the cartesian equation of the curve of x=t^2-3,y=t+1, for -2≤y≤4.

Answer 1

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.

Answer 2

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