`x=root(4)(t) , y=8-t` 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 equation is traced as the parameter increases is called the...

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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 equation is traced as the parameter increases is called the orientation imposed on the curve by the equation.

Now let's eliminate the parameter t , to write the corresponding rectangular equation,

Given parametric equations are :

`x=root(4)(t)`   -----------------  (1)

`y=8-t`    ----------------   (2)

From equation 1,

`t=x^4`

Substitute t in the equation 2,

`y=8-x^4`  , is the rectangular equation of the given parametric equations.

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