(a) sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases

(b) Eliminate the parameter to find the Cartesian equation of the curve

`x=t^2,`   `y=t^3`

Expert Answers

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The parametric variable t may take any real values. As t increases from `-oo` to 0, x decreases from `+oo` to 0 and y increases from `-oo` to 0. For positive t x increases from 0 to `+oo` and y, too. Note that x is always non-negative.

a) please look at the attached picture. It shows points for `t=0, +-1/2, +-7/10, +-9/10, +-1, +-1.5.` The direction on the curve is also shown.

b) express y from the equation `y=t^3,` it is `t=root(3)(y).` Then substitute it to `x=t^2` and obtain `x=root(3)(y^2).` This is the answer. We can also express this as  `y=+-x^(3/2).`


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