Traditional Culture Encyclopedia - Photography major - The distance between two fixed points is 6, and the sum of the squares of the distances from point M to these two fixed points is 26. Find the trajectory equation of point M.
The distance between two fixed points is 6, and the sum of the squares of the distances from point M to these two fixed points is 26. Find the trajectory equation of point M.
Solution: Assume two fixed points: A and B, the midpoint o between AB is the coordinate origin, OB is the x-axis, and a rectangular coordinate system is established.
Rule: According to the meaning of the question, the agenda of moving point M is: (x - 3)^2 + y^2 + (x + 3)^2 + y^2 = 26.
The equation is simplified to: Y^2 + x^2 = 4 = 2^2 (that is, the circumference of the garden with point O as the center and 2 as the radius)
Answer: Point M The trajectory equation is: Y^2 + x^2 = 4 (that is, the circle circumference with point O as the center and 2 as the radius).
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