Teacher worldbl: the distance from the moving point m (x, y) to the y-axis is less than the distance from it to the fixed point (2,0). Find the trajectory equation of the moving point m (x, y)

The distance from the moving point m (x, y) to the y-axis is less than the distance from it to the fixed point (2,0),
Then the distance from the moving point m (x, y) to the straight line x = - 2 is equal to the distance from it to the fixed point (2,0)
So the trajectory of M is a parabola with a fixed point (2,0) as the focus and x = - 2 as the guide line,
So p / 2 = 2, P = 4
The equation is Y & # 178; = 2px = 8x, that is Y & # 178; = 8x
In addition, the drawing shows that the distance from the point on the negative half axis of the X axis to the Y axis is less than 2,
That is, y = 0 (x ≤ 0) also satisfies the condition

Given that the distance between point m and X axis and the distance between point m and point F (0,4) are equal, the trajectory equation of point m is obtained

If M (x, y) is set as a moving point, then the distance between M and X axis and the distance between M and f (0, 4) are equal, that is, the trajectory equation of M is y = 18x2 + 2

What is the trajectory equation of the moving point whose distance to the point (1,0) is equal to the distance to the x-axis

If x.y is set as a moving point, the following results can be obtained
√(x-1)²+y²=|y|;
（x-1）²+y²=y²;
(x-1)²=0;
x-1=0;
x=1;
The trajectory of moving point is x = 1;
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The distance from the moving point P (x, y) to the fixed point a (3,4) is 1 more than the distance from P to the X axis?
We should consider the positive and negative of Y

Obviously, y must be a positive value. If you draw a coordinate system, if y is negative, then the distance from P to a is at least 4
The distance from P to a is equal to the distance from P to y = - 1, so this is a parabola. P = the distance from point a to y = - 1, that is 5. Considering the translation of the parabola, the equation is 2 * 5 (y-1.5) = (x-3) ^ 2. You can verify it
By the way, this is a basic problem in senior high school. Don't listen to those people's talk about solving equations. Actually, this problem is to study the definition of parabola

Teacher worldbl: the distance from the moving point m (x, y) to the y-axis is less than the distance from it to the fixed point (2,0). Find the trajectory equation of the moving point m (x, y)