The question goes:

Find the y-intercept of the normal to the parabola y=x^2 at the point

(a,a^2), where a cannot equal 0. Find the limit of this y-interept as a approaches 0. For each b>0 determine the number of normals that can be drawn from the point (0,b) to the parabola y=x^2; justify your answer.

So far i have gotton that the y intercepts= 1/2+a^2, however, i'm not sure what the limit of the y intercept as a approaches 0. Additionally, i can't figure out how to determine the amount of normals.

Thanks a Lot

Willie Li