Locus

**lance** · February 19th 2010, 10:38 PM

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!

**Prove It** · February 19th 2010, 11:47 PM

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.

**qmech** · February 20th 2010, 10:57 AM

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

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