eliminate the parameter from the subsequent set

Question

Eliminate the parameter from the subsequent set of parametric equations.

X = t² + t

Y = 2t - 1

Solution:

One of the very easy ways to eliminate the parameter is to just solve one of the equations for the parameter (t, in this case) and substitute that into another equation. Note: when this may be the easiest to eliminate the parameter, it's generally not the best way as we will see soon enough. In this case we can simply solve y for t.

T = ½ (y+1)

Plugging this into the equation for x provides,

X = (1/2 (y+1))² + ½ (y+1)

= ¼ y² + y + ¾