`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.

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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`

 

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