How to find direction vector of a ray after getting reflected from the surface of an ellipsoid?

Question

I am developing a Monte Carlo simulation for an elliptical reflector. A light source is usually placed at the f1 of the ellipsoid and all rays after getting reflected from the reflector pass through f2. But we need to check the effects of changing the position of the source. Hence, I need to know that what will be the direction vector of reflected ray if a ray is emitted from an arbitrary point inside the ellipsoid. If I know the direction vector of the reflected ray then I can find the points trough which it will pass after getting reflected ( I want this!). I know how to find the point of intersection between the ellipsoid and incoming rays. Using this intersection point, I have tried finding out the angle between the tangent plane and the incoming ray. We know the angle of incidence and reflection will be the same. But I am unable to solve the problem. All I want is the direction vector for the reflected ray. Any help will be appreciated. Thanks! P.S: I am using MATLAB