# Locus

• Feb 19th 2010, 11:38 PM
lance
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.

• Feb 20th 2010, 12:47 AM
Prove It
Quote:

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.

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.
• Feb 20th 2010, 11:57 AM
qmech
Quote:

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.

$\sqrt( (x-5)^2+(y-2)^2)$
$|y|$
$\sqrt( (x-5)^2+(y-2)^2) = \frac{2}{3}|y|$