You can create the extended curve by creating a curve through points. Make the end of the curve connecting to the existing curve tangent. You will have to create a point or something to connect the other end.
You can also make a surface as suggested through the curve and extend the surface.
I got a suggestion .. you can use the composite command on the datum curve menu.. select the exact mode, you will see the selection for curve extension.. kindly enter the length you want.