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The chord of contact of tangents drawn from a point on the circle x^{2}+y^{2}=a^2 to the circle x^{2}+y^{2}=4 touches the circle x^{2}+y^{2}=1, then find the value of a (given a > 0)

Option: 1

2


Option: 2

3


Option: 3

4


Option: 4

5


Answers (1)

best_answer

\\\text{Let P}(a \cos \theta, a \sin \theta) \text{ be any point on the circle }x^{2}+y^{2}=a^{2}.\\ \text{Therefore, chord of contact of this point with respect to circle }x^2+y^2=4\,\,is\,\, \\ a x \cos \theta+a y \sin \theta=4 ...(i)

\\ \text{Since the line (i) is a tangent to the circle } x^2+y^2=1\\ |\frac{0+0-4}{\sqrt{a^{2} \cos ^{2} \theta+a^{2} \sin ^{2} \theta}}|=1 \\ \Rightarrow 4=a \times 1 \\ \Rightarrow a=4

 

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