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Equation of a tangent to the circle with centre $(2, - 1)$ is $3 x + y = 0$ , the square of length of
the tangent to the circle from $(23, 17)$ is $λ$ then $2 λ$ is..........

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answer is 1525.

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Detailed Solution

r = $| \frac{3 \times 2 + 1 (- 1) + 0}{\sqrt{9 + 1}} | = \frac{5}{\sqrt{10}}$
Equation of circle ;- ${(x - 2)}^{2} + {(y + 1)}^{2} = \frac{5}{2}$
$S_{11} = [{(23 - 2)}^{2} + {(17 + 1)}^{2}] - \frac{5}{2} = \frac{1525}{2}$

$λ = \frac{1525}{2}$

$2 λ = 1525$

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