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JEE Math Practice Question

If the circle $$x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}$$ passes through the point $$(6,1)$$ and its centre lies on the line $$x-2 c y=8$$, then the length of intercept made by the circle on $$x$$-axis is :

  1. A.$$\sqrt{11}$$
  2. B.4
  3. C.3
  4. D.$$2 \sqrt{23}$$

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