You can read the user guide (PDF) by clicking on the question mark in the top-right corner and selecting Desmos User Guide.
Just enter the following:
((1/3)*k(\sinh (t)-8\sinh (0.5t)+3t),k(\sinh (t)-t))
Below the equation a message appears offering to add a slider for $k$ (since it's a free variable). After clicking $k$, another message appears below the equation saying "domain: $0\le t\le 1$". Clicking it allows selecting the interval where $t$ ranges.