Question

How do you write the cartesian equation for x = t - 2 and y = -(t²) + t + 1?

Answer 1

Cartesian equation for given parametric equation is `x^2+3x+y+1=0`, which is the equation of a parabola.

Explanation:

As `x=t-2`, we have `t=x+2`

Hence `y=-t^2+t+1` can be written as `y=-(x+2)^2+x+2+1`

or `y=-x^2-4x-4+x+2+1`

or `x^2+3x+y+1=0`, which is the equation of a parabola.

graph{x^2+3x+y+1=0 [-10, 10, -5, 5]}