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Find two different sets of parametric equations for the following equation: y= (1/(x^3)) I need the answers to this.

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2 Answers

If you have an equation y = f(x) then you can define x=g(t), in which case substituting into the equation for y, you get y=f(g(t)). The only constraint on the choice on the function g(t) is that the range of g(t) includes the entire domain of f(x). That way the graph of the parametric equations is the entire graph, not a partial one, of the original equation.

In your case, the two answers you gave are correct, as are many others: y = 1/x3 = 1/(2t)3 = 1/(8t3) in the first pair of equations, and y = 1/x3 = 1/t3 in the second pair of equations.

Good job.

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It's been awhile since I've done parametric equations, and with that disclaimer out of the way, here are my thoughts: 

I agree with the {x=t, y=(1/t3)} . I'm thinking the second one could be {(1/x)=t, y=t3)}. 

With x = 2t, you could then include additional possibilities of x= 3t, x = 4t, and so on.