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If a line through P(–2, 3) meets the circle $x^{2} + y^{2} - 4 x + 2 y + k = 0$ at A and B such that PA.PB = 31 then the radius of the circle is

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answer is A.

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Detailed Solution

$PA . PB = S_{11} 31 = 4 + 9 + 8 + 6 + k \Rightarrow 31 = 27 + k \Rightarrow k = 4 N o w r = \sqrt{4 + 1 - 4} = 1$

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