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The length of the intercept on the line $4 x - 3 y - 10 = 0$ by the circle $x^{2} + y^{2} - 2 x + 4 y - 26 = 0$ is

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$2 \sqrt{31}$

$10 \sqrt{31}$

$\sqrt{31}$

answer is B.

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Detailed Solution

$x^{2} + y^{2} - 2 x + 4 y - 26 = 0$
$C = (1, - 2), r = \sqrt{1 + 4 + 26} = \sqrt{31}$
Intercept is the diameter, length $= 2 \sqrt{31}$

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