From a point (sin⁡θ,cos⁡θ) , if three normals can be drawn  to the parabola y2=4ax, then the value of a is

Point (sin⁡θ,cos⁡θ) lies on the circle x2+y2=1∀θ∈R Now, three normals can be drawn to the parabola y2=4ax if x=|2a| meets this circle.  Hence, we must have cos⁡θ>|2a| or 0<|2a|<1 or 0<|a|<12 or a∈−12,0∪0,12