Question

X = t4, y = ln(t) (a) eliminate the parameter to find a cartesian equation of the curve.

Answer 1

I guess when you say you want a cartesian equation of the curve, you would have to express them in cartesian coordinates of x and y. Thus, you must get rid of the variable t. The solution is as follows:

x = t⁴
y = ln(t)

e^y = e^(lnt)
e^y = t

Substuting this to the first equation,
x = (e^y)⁴
x = e^4y