x=2t^2 , y=t^4+1 Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.

Draw a table for different values of t and plot the corresponding points (x,y) obtained from the table. Connect the points to a smooth curve.(Refer the attached image).
The direction in which the graph of a pair of parametric equations is traced as the parameter increases is called the orientation imposed on the curve by the equation.
Note:Not all parametric equations produce curve with definite orientation. The point tracing the curve may leap around sporadically or move back and forth failing to determine a definite direction.
Given parametric equations are:
x=2t^2  ------------------(1)
y=t^4+1  ----------------(2)
Now let's eliminate the parameter t,
From equation 1,
t=(x/2)^(1/2)
Substitute t in equation 2,
y=((x/2)^(1/2))^4+1
y=(x/2)^(4/2)+1
y=(x/2)^2+1
y=x^2/4+1