# Math Help - Locus of Points

1. ## Locus of Points

(1) Point P is located on line AB.

(a) Describe the locus of points that are 3 units from line AB and (b) 5 points from point P.

(2) How many points satisfy both conditions in part (a) above?

2. Originally Posted by magentarita
(1) Point P is located on line AB.

(a) Describe the locus of points that are 3 units from line AB and (b) 5 points (maybe units?) from point P.

(2) How many points satisfy both conditions in part (a) above?
a) The locus of all points which are 3 units from a straight line are two parallels: One "above" and one "below"

b) The locus of all points with a constant distance to a fixed point is a circle.

Since $P \in (AB)$ and the radius of the circle is greater than the distance of the parallels to (AB) you'll get 4 points.

3. ## ok

Originally Posted by earboth
a) The locus of all points which are 3 units from a straight line are two parallels: One "above" and one "below"

b) The locus of all points with a constant distance to a fixed point is a circle.

Since $P \in (AB)$ and the radius of the circle is greater than the distance of the parallels to (AB) you'll get 4 points.
Thanks for the great tips.