NTA Abhyas JEE Main2020MathematicsCirclePractice

The perimeter of the locus of the point at which the two circles x 2 + y 2 = 1 and x - 4 2 + y 2 = 4 subtend equal angles is

Options

A4 3 π
B8 3 π
C2 3 π
D16 3 π

Correct answer

D. 16 3 π

Step-by-step solution

sin ⁡ θ = 1 h 2 + k 2 = 2 h - 4 2 + k 2 ⇒ h 2 - 8 h + 16 + k 2 = 4 h 2 + 4 k 2 ⇒ 3 x 2 + 3 y 2 + 8 x - 16 = 0 Radius of the circle is 4 3 2 + 16 3 = 16 + 48 9 = 8 3 ⇒ Perimeter is equal to 16 π 3

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