If the distance from the moving point m (x.y) to the fixed point (1,1) is equal to the distance from m to the fixed line X-Y plus 1 equals 0, then the trajectory equation of the moving point m is? If the distance from the moving point m (x.y) to the fixed point (1,1) is equal to the distance from m to the fixed line X-Y plus 1 equals 0, then the trajectory equation of the moving point m is

If the distance from the moving point m (x.y) to the fixed point (1,1) is equal to the distance from m to the fixed line X-Y plus 1 equals 0, then the trajectory equation of the moving point m is? If the distance from the moving point m (x.y) to the fixed point (1,1) is equal to the distance from m to the fixed line X-Y plus 1 equals 0, then the trajectory equation of the moving point m is

Under the root sign [(x-1) square + (Y-1) square] = (X-Y + 1) absolute value / root sign 2 x square - 6x + y square - 2Y + 2XY + 3 = 0

If the sum of distances from a moving point P (x, y) to two fixed points a (- 1,0) and B (1,0) is a fixed value m, try to find the trajectory equation of point P
We should have a more detailed thinking

(x+1)^2+y^2+(x-1)^2+y^2=m
2x^2+2y^2+2=m
x^2+y^2=(m-2)/2

If the distance from the moving point P to the point a (8,0) is twice that to the point B (2,0), then the trajectory equation of the moving point P is ()
A. x2+y2=32B. x2+y2=16C. （x-1）2+y2=16D. x2+（y-1）2=16

Let P (x, y), then we can get 2 (x − 2) 2 + y2 = (x − 8) 2 + Y2 from the meaning of the question, and we can get x2 + y2 = 16 from the simplification

The distance from the moving point P to the point a (0,8) is 1 greater than that to the straight line y = - 7
I remember a theorem. If the distance from a moving point to a is greater than that from a straight line, it is hyperbola! But why can't we use it here? The trajectory equation of P point is parabola!
I don't know which genius taught me!

P(x,y)
The distance from P to point a (0,8) is 1 greater than that to the straight line y = - 7
√[(x^2+(y-8)^2]-|y+7|=1
√[(x^2+(y-8)^2]=1+|y+7|
x^2-30y+14=2|y+7|
y≥0,x^2=32y
y≥1,x^2=28(y-1)