# Math Help - Locus

1. ## Locus

Determine the equation of the locus of a point which moves so that its distance from P(5,2) is two-thirds its distance from the x-axis.

Please help me solve this problem and show the solution... Thanks!

2. Originally Posted by lance
Determine the equation of the locus of a point which moves so that its distance from P(5,2) is two-thirds its distance from the x-axis.

Please help me solve this problem and show the solution... Thanks!
Hint: a parabola is the locus of points that are equidistant from a point (the focus) and a line (the directrix). I'd advise you to research how to find the equation of a parabola using the focus and directrix.

3. Originally Posted by lance
Determine the equation of the locus of a point which moves so that its distance from P(5,2) is two-thirds its distance from the x-axis.

Please help me solve this problem and show the solution... Thanks!
Treat this as a word problem:

Distance from P(5,2) =
$\sqrt( (x-5)^2+(y-2)^2)$

Distance from x-axis =
$|y|$

So the locus is:
$\sqrt( (x-5)^2+(y-2)^2) = \frac{2}{3}|y|$