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  4. The number of real circles cutting orthogonally the circle x2 + y2 + 2x - 2y + 7 = 0 is

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Q. The number of real circles cutting orthogonally the circle $x^2 + y^2 + 2x - 2y + 7 = 0$ is

KCETKCET 2013Conic Sections

Solution:

Given, equation of circle is
$x^{2}+y^{2}+2 x-2 y+7=0$
Here, radius of the circle
$=\sqrt{(1)+(-1)^{2}-7} $
$=\sqrt{1+1-7}=\sqrt{-5} $
$=$ imaginary
$\therefore $ Given circle is an imaginary circle.
Hence, number of real circles cutting orthogonally the given imaginary circle is zero.