# Coordinate Geometry-13

### From Homeworkwiki

**A point moves so that its distance from the point (2, 0) is three times its distance from (-3, 0). Find the locus of the point.**

**Solution:** Let A be the point (2, 4)

Let B be the point (- 3, 0)

Let P be the point (x, y)

PA = 3 PB

=> √(x - 2)^{2} + (y - 4)^{2} = √3 [ (x + 3)^{2} + (y - 0)^{2} ]

i.e. (x - 2)^{2} + (y - 4)^{2} = 9 [ (x + 3)^{2} + (y - 0)^{2} ] [squaring both sides]

i.e. x^{2} + y^{2} - 4x - 8y + 20 = 9 [x^{2} + y^{2} + 6x + 9 ]

i.e. 8x^{2} + 8y^{2} + 58x + 8y + 61 = 0 is the equation of the locus.