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Find the equation of the locus of the centres of all circles that intersect each of the circles x² + y² + 4x - 6y + 9 = 0 and x² + y² - 5x + 4y - 2 = 0 at right angles.
- 9x + 10y - 7 = 0
- x - y + 2 = 0
- 9x - 10y + 11 = 0
- 9x + 10y + 7 = 0
Correct answer: 9x - 10y + 11 = 0
Solution
The correct option represents the locus of centers of circles that intersect the given circles at right angles, which is derived from the condition that the power of the point (the center of the new circle) with respect to each of the original circles must be equal to the square of the radius of the new circle.
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