Parametric equations?

Question

eliminate t from equations X=t² y=t³ and form a cartesian equ.

X=3sinΦ y=3cosΦ eliminate Φ and form a cartesian equation.

xy=5 is equivalent to y=t and x=f(t). Find f(t)

any help appreciated

Answer 1

First problem:
If X=t², then t = +-Sqrt(x).
Now, with y=t³, we substitute the above to find that y=+-x^(3/2).

A different way to get a cartesian equation is to cube "X=t²" and square "y=t³", getting X³=Y².


Second problem: square both equations.
x² = 9sin²Φ, y²=9cos²Φ.
Now x²+y² = 9sin²Φ + 9cos²Φ = 9.

Third problem:
If xy=5 and y=t, then xt=5. So, x=5/t. f(t)=5/t.