Sure!
1. The first part of the problem asks for the parametric equation for 'x', which is represented as x = 2t. To get this, we simply multiply the parameter 't' by 2. This forms our equation for x.
2. The second part of the problem is to determine the parametric equation for y. Here, we square the parameter 't' and then subtract 2 from the result, which gives us the equation y = t^2 - 2.
By combining these two parametric equations, we get the form (x, y) where x represents all possible x-positions and y represents all corresponding y-positions.
With the equations x = 2t and y = t^2 - 2, you can substitute any real number for 't' and find the corresponding (x, y) coordinates. These parametric equations define a family of points in the coordinate system that can represent a curve, a line, or another geometric object. In this specific case, the definitions x = 2t and y = t^2 - 2 describe a parabola.