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Find the equation of the circle that cuts each of the following three circles orthogonally: x² + y² - 2x + 3y - 7 = 0, x² + y² + 5x - 5y + 9 = 0, x² + y² + 7x - 9y + 29 = 0.
- x² + y² - 16x - 18y - 4 = 0
- x² + y² + 16x + 18y - 4 = 0
- x² + y² - 16x - 18y + 4 = 0
- x² + y² - 8x - 9y - 4 = 0
Correct answer: x² + y² - 16x - 18y - 4 = 0
Solution
Applying 2g*gi + 2f*fi = c + ci to the three circles gives a linear system whose solution is g = -8, f = -9, c = -4, i.e. x² + y² - 16x - 18y - 4 = 0.
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