Do you wish to include friction? A frictionless analysis gives a parabola whose curvature depends on the ball's initial velocity and the degree of the slope.

Specifically, if we let the Cartesian plane be the plane that is sloped 1 degree (pi/180 radians) from the positive y-axis to the negative y-axis, and we hit the ball along the negative x-axis from the origin, the ball will describe the path

\(\displaystyle y = -\left(\frac{g\sin\left(\frac{\pi}{180}\right)}{2v^2}\right)x^2\)

g is the acceleration due to gravity where the green is located. At sea level, it is usually 9.8 meters/(second^2). v is the initial velocity with which the ball is hit along the negative x-axis. You will need to find the correct v to deviate from the hole in the correct way:

If the hole is located at (-R, 0), then you must solve the equation

\(\displaystyle R = \frac{2v^2\tan\left(\frac{\pi}{18}\right)}{g\sin\left(\frac{\pi}{180}\right)}\)

to get the initial velocity v necessary to accomplish your deviation of 10 degrees (pi/18 radians).

If you simply want the curve and you don't actually care about v, simply replace v with the relevant function of R in the original equation:

\(\displaystyle y = -\left(\frac{\tan\left(\frac{\pi}{180}\right)}{R}\right)x^2\)

If you want to include non-zero friction, the result is a solution of a differential equation that is no longer a parabola.