The distance between two fixed points is 6, and the sum of squares of the distances from point M to these two fixed points is 26. Find the trajectory equation of point m.

Solution: Take the straight line passing through two fixed points F 1 and F2 as the X axis, the line segment F 1 and the vertical line of F2 as the Y axis, and establish a rectangular coordinate system. The sum of the squares of the distances from f1(-3,0), F2 (3 3,0) and M (x, y) to these two fixed points is 26.

[(x-3)^2+y^2]+[(x+3)^2+y^2]=26

2x^2+2y^2+ 18=26

X 2+y 2 = 4 is the trajectory equation of m.

The trajectory of m is a circle with the origin o (0,0) as the center and 2 as the radius.

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