The number of normals that can be drawn through the point (2,0) to the parabola $y^2 = 7x$ is
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For a parabola $y^2=4ax$, the number of distinct normals that can be drawn from a point $(h,k)$ is determined by the number of real roots of the cubic equation $k = mh - 2am - am^3$. A simpler condition is that if $h \leq 2a$, there is always exactly one real normal.