數學問題 Locus

Consider all the circles passing through P(6,7) and Q(-2,3). Find the equation of the locus of their centres.


Let (x, y) be the centres of the required circles.

The distance between (x, y) and P or Q is the radius of the circle.
√[(x - 6)² + (y - 7)²] = √[(x + 2)² + (y - 3)²]
x² - 12x + 36 + y² - 14y + 49 = x² + 4x + 4 + y² - 6y + 9
16x + 8y - 72 = 0
2x + y - 9 = 0

Equation of the locus of the centres:
2x + y - 9 = 0