# Compound Locus

• Jan 22nd 2007, 05:05 PM
symmetry
Compound Locus
(1) What is a locus.

(2) What is compound locus?

QUESTION:

Two points A and B are 6 units apart. How many points are there that are equidistant from both A and B and also 5 units from A?
• Jan 22nd 2007, 11:02 PM
ticbol
Quote:

Originally Posted by symmetry
(1) What is a locus.

(2) What is compound locus?

QUESTION:

Two points A and B are 6 units apart. How many points are there that are equidistant from both A and B and also 5 units from A?

Locus and compound locus?
For definitions, search Google or Wikipedia or Yahoo.

---------------
The Question:

The locus of points that are 5 units from A is a circle whose center is A.

The locus of points that are equidistant from both A and B is the perpendicular bisector of line AB.

The intersection of these two loci answers your question.

The equation of the circle whose center is A and whose radius is 5 units, if the origin (0,0) is at A, is
x^2 +y^2 = 5^2
x^2 +y^2 = 25 -----------first locus.

If A again is the origin (0,0), the perpendicular bisector of line AB is
x = 6/2
x = 3 ---------------------second locus

Their intersection:
Substitute 3 for x in the first locus,
3^2 +y^2 = 25
y^2 = 25 -9 = 16
y = +4 or -4

So there are two intersection points, (3,4) and (3,-4)

Therefore, two points. -----------answer.
• Jan 23rd 2007, 03:32 AM
symmetry
ok
A locus could be a line, an equation, etc?
• Jan 23rd 2007, 04:36 AM
ticbol
Quote:

Originally Posted by symmetry
A locus could be a line, an equation, etc?

Have you searched at least Google for "locus"?

Here is one from Google:
"A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point is a circle, and the set of points in three-space equidistant from a given point is a sphere."

Locus means the locations/positions of a set of points satisfying some condition.

"locus" ---"location"

And, yes, a locus of points can be a line, a curved line, a surface,.....
• Jan 23rd 2007, 06:22 PM
symmetry
ok
Okay...I will study locus more deeply.