The equations of two circles are $x^{2} + y^{2} - 26 y + 25 = 0$ and $x^{2} + y^{2} = 25$ . Then

they touch each other

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they cut each other orthogonally

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one circle is inside the other circle

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none of these

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Solution

The correct option is B they cut each other orthogonally
$C 1 (13, 0)$ and $r_{1} = \sqrt{13^{2} - 25} = 12$
$C 2 (0, 0)$ and $r_{2} = 5$
$C 1 C 2 = 13$ and $r_{1} + r_{2} = 17$
Since, $C 1 C 2 < r_{1} + r_{2}$
Therefore, two circles intersect each other
Since, $2 g g^{'} + 2 f f^{'} = c + c^{'}$
Therefore, given circles are orthogonal
Ans: B

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