In Geiger-Marsden scattering experiment, the trajectory traced by an $\alpha$-particle depends on:

Trajectory of $\alpha$-particle depends on impact parameter which is the perpendicular distance of the initial velocity vector of the $\alpha$-particle from the center of the nucleus. 

The extent of scattering (angle of scattering) is inversely proportional to the impact parameter.

For small impact parameter, $\alpha$-particle close to the nucleus and suffers larger scattering.