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The length of the tangent drawn from any point
on the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ to the circle
$x^{2} + y^{2} + 2 g x + 2 f y + c_{1} = 0$ is

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Correct option is D

Let (α,β) be a point on x2+y2+2gx+2fy+c=0 Then, the length of the tangent from (α,β) tox2+y2+2gx+2fy+c1=0 is given by l=α2+β2+2gα+2fβ+c1Since (α,β) lies on x2+y2+2gx+2fy+c=0 ∴ α2+β2+2gα+2fβ=−cHence l=c1−c

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The length of the tangent drawn from any pointon the circle x2+y2+2gx+2fy+c=0 to the circlex2+y2+2gx+2fy+c1=0 is

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The length of the tangent drawn from any point
on the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ to the circle
$x^{2} + y^{2} + 2 g x + 2 f y + c_{1} = 0$ is