Question

Consider the following. x = e4t, y = t + 7

Eliminate the parameter to find a Cartesian equation of the curve.

Answer 1

y = 7 +ln(x)/4

Explanation:

Maybe your parameterized equation is ...

(x, y) = (e^(4t), t +7)

Using t = y-7, we can substitute for t in the expression for x:

x = e^(4(y -7))

ln(x) = 4(y -7)

ln(x) +28 = 4y

y = 7 +ln(x)/4