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$From a point (\sin θ, \cos θ), if three normals can be drawn to the parabola y^{2} = 4 a x, then the value of a is$

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(1/2,1)

[−1/2,0)

[−1/2,1]

(−1/2,0)∪(0,1/2)

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detailed solution

Correct option is D

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

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

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$From a point (\sin θ, \cos θ), if three normals can be drawn to the parabola y^{2} = 4 a x, then the value of a is$