The number of real circle cutting orthogonally the circle $x^{2} + y^{2} + 2 x - 2 y + 7 = 0$ is _____

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Infinitely many

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Solution

The correct option is A 0
Given circle is, $x^{2} + y^{2} + 2 x - 2 y + 7 = 0$
$\Rightarrow (x^{2} + 2 x + 1) + (y^{2} - 2 y + 1) + 5 = 0$
$\Rightarrow (x + 1)^{2} + (y - 1)^{2} = - 5$
So above circle is not real circle, since radius is imaginary
Hence it does not have orthogonal circle

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