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The points of contact of tangents to the circle $x^{2} + y^{2} = 25$ which are inclined at an angle of $30 °$ to the $x -$ axis are

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(±5/2, ±1/2)

(±1/2, ±5/2)

(∓5/2,∓1/2)

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detailed solution

Correct option is D

The equation of a tangent of slope m to the circle x2+y2=a2 is y=mx±a1+m2 and the coordinates of point of contact are ∓am1+m2,±a1+m2 Here, a=5 and m=tan 30=1/3.So, the coordinates of the points of contact are ∓52,±532

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The points of contact of tangents to the circle x2 + y2 = 25 which are inclined at an angle of 30° to the x-axis are

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The points of contact of tangents to the circle $x^{2} + y^{2} = 25$ which are inclined at an angle of $30 °$ to the $x -$ axis are