SOLUTION: 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

Algebra.Com
Question 1189327: 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
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
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
~~~~~~~~~~~~~~ 

An equation of the locus is

     = |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.


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

         No one of the listed in the options list.

Solved.



RELATED QUESTIONS

find the equation of the path of a point that moves so that its distance from (4,0) is... (answered by Fombitz)
Find the equation of the locus of a point which moves so that its distance from the point (answered by richwmiller)
Find the equation of the locus of a point which moves so that its distance from the... (answered by richwmiller)
Derive the equation of the locus of a point P(x,y) which moves so that its distance from... (answered by josgarithmetic,ikleyn,greenestamps)
Please explain how you do this question: Derive the equation of the locus of a point... (answered by stanbon)
A point P(x,y) moves so that its distance from the point K(2,5) is twice its distance... (answered by MathLover1)
Hi What is the equation of the locus of a point P(x, y) that moves according to the... (answered by greenestamps)
A curve is traced by a point (x,y) which moves such that its distance from the point... (answered by greenestamps)
Find the equation of the locus of a point which moves so that its distance from the point (answered by josgarithmetic,ikleyn)