# Coordinate Geometry-12

### From Homeworkwiki

**Find the equation of the locus of the point, such that its distance from the two points (0, a) and (0, -a) are equal.**

**Solution:** Let A be the point (0, a) and B be the point (0, -a). Let P(x, y) be any point on the locus. Therefore, PA = PB

[ √(x - 0)^{2} + (y - a)^{2} ] = √[ (x - 0)^{2} + (y + a)^{2} ]

Squaring, x^{2} + (y - a)^{2} = x^{2} + (y + a)^{2}

Therefore, (y + a)^{2} - (y - a)^{2} = 0 i.e. 4ay = 0

y = 0 which is the x-axis

Therefore, the required locus is the x-axis.