eliminate the parameter and write a rectangular equation for
x=(t^2)+3
y=2t
from the 2nd, t = y/2
into the 1st:
x = (y^2/4 + 3
4x = y^2 + 12
looks like a parabola.
To eliminate the parameter and write a rectangular equation, we need to express x and y in terms of each other without using t. In this case, we have:
x = t^2 + 3
y = 2t
To eliminate t, we can solve the second equation for t and substitute it into the first equation.
From the second equation, we can express t in terms of y:
t = y/2
Now, substituting this value of t into the first equation:
x = (y/2)^2 + 3
x = (1/4)y^2 + 3
Therefore, the rectangular equation for the given parametric equations is:
x = (1/4)y^2 + 3