Question 1189327
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A point moves so that its distance from the point (2,-1) is equal to its distance from the x-axis. 
Find the equation of the locus.
a. x^2 - 4x - 4y + 4 = 0
b. y^2 - 4x - 2y + 5 = 0
c. x^2 - 4x - 2y + 5 = 0
d. x^2 + 4x - 2y + 5 = 0
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An equation of the locus is

    {{{sqrt((x-2)^2+(y+1)^2)}}} = |y|.    (notice the absolute value sign in the right side !)


Square both sides of the equation

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


Simplify

    x^2 - 4x + 4 + y^2 + 2y + 1 = y^2

    x^2 - 4x + 2y + 5 = 0.


<U>ANSWER</U>.  The equation of the locus is  x^2 - 4x + 2y + 5 = 0.

         No one of the listed in the options list.
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Solved.