Find the y intercept of the normal to the parabola $\displaystyle y=x^2$ at the points $\displaystyle (a,a^2)$, where a does not equal to 0.

Find the limit of this y intercept 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 $\displaystyle y=x^2$