The tangent from P is always vertical if 

yP = 0.

If a point P is such that yP = 0, then the tangent line to the elliptic curve at P is vertical and does not intersect the elliptic curve at any other point. 

By definition, 2P = O for such a point P. 

If one wanted to find 3P in this situation, one can add 2P + P. This becomes P + O = P Thus 3P = P. 

3P = P, 4P = O, 5P = P, 6P = O, 7P = P, etc.