The trajectory equation of the point on the plane where the absolute value of the distance difference between two fixed points F1 (- 7,0) F2 (7,0) is equal to 10 2c=14 c=7 c^2=49 2a=10 a=5 a^2=25 b^2=49-25=24 x^2/25+y^2/24=1 But the answer is x ^ 2 / 25-y ^ 2 / 24 = 1 Shouldn't the + sign be used in the middle? Is the trajectory equation + or -?

The trajectory equation of the point on the plane where the absolute value of the distance difference between two fixed points F1 (- 7,0) F2 (7,0) is equal to 10 2c=14 c=7 c^2=49 2a=10 a=5 a^2=25 b^2=49-25=24 x^2/25+y^2/24=1 But the answer is x ^ 2 / 25-y ^ 2 / 24 = 1 Shouldn't the + sign be used in the middle? Is the trajectory equation + or -?

The distance difference is the most important factor
So it's a hyperbola
And the focus is on the y-axis
So it's x ^ 2 / 25-y ^ 2 / 24 = 1

The absolute value of the distance difference between two fixed points F1 (- 2,0) F2 (2,0) in the plane is 2, and the locus of the point is 2
Like the title,

If we know that F1 and F2 are two fixed points, the absolute value of F1F2 is equal to 6, and the absolute value of MF1 + MF2 is equal to 6, then the trajectory of moving point m is

|MF1 | + | MF2 | = 2A = 6. So a = 3. | F1F2 | = 6 = 2C. C = 3. B = 0~

Let F1 and F2 be fixed points, the absolute value of F1F2 = 8, the absolute value of MF1 + the absolute value of MF2 = 6, then the trajectory of the moving point m is

The title of the building is wrong, according to the triangle trilateral relationship
|MF1|+|MF2|≥|F1F2|
Contradiction, if two data change over, there is an answer
According to the definition of ellipse, there are
2C = 6 (focal length)
2A = 8 (long axis)
b²=a²-c²=7
So the trajectory equation of point m is
x²/16+y²/7=1