Question

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

• A. 0
• B. 1
• C. 2
• D. infinitely many

Answer 1

Answer: (A)

0

Answer 2

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.