The point from which the lengths of tangents to the three circles $x^{2} + y^{2} - 4 = 0, x^{2} + y^{2}$ -2x $+ 3 y = 0$ and $x^{2} + y^{2} + 7 y - 18 = 0$ are equal is

(2, 5)

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(3, 4)

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(4, 3)

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(5, 2)

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Solution

The correct option is D $(5, 2)$
radical centre is a locus of point from which equal length
of tangent can be draw to circles.
So, $s_{1} - s_{2} = 0 \Rightarrow$ radical axis
$2 x - 3 y - 4 = 0 - - (1)$
and $s_{1} - s_{3} = 0 \Rightarrow$ radical axis
$- 7 y + 14 = 0 - - (2)$
from (1) & (2), $y = 2$ and $x = 5$
So, radical centre is $(5, 2)$

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