If it is known: (1): the distance from one point to another is equal to the distance from this point to another straight line-this is a "parabola" equation (principle: the distance from a point on a parabola to the directrix = the distance from this point to the focus of the parabola, that is, the distance from one point to another is equal to the distance from this point to another straight line).
(2): The sum of the distances from one point to the other two points is a constant-it is an "ellipse" equation (principle: the sum of the distances from one point P to two focal points on an ellipse =2a, that is, the sum of the distances from one point to the other two points is a constant).
(3): The difference between the distances from one point to the other two points is a constant, that is, the hyperbolic equation (principle: the absolute value of the difference between the distances from one point P to two focal points on a hyperbola =2a, that is, the difference between the distances from one point to the other two points is a constant).
(4): The ratio of the distance from one point to the other two points is a fixed value-it is a "circle" equation (the principle is hard to say, many symbols can't be typed. . . . . . . . . . ) is to use the point-to-point distance formula for a generation, and then compare it with a fixed value, and a series of equations will come out.
I am a senior three, and it takes me an hour to understand this kind of problem. I hope to adopt it, hehe. Math needs hard work! ! !