(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?

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- January 22nd 2007, 04:05 PMsymmetryCompound 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? - January 22nd 2007, 10:02 PMticbol
Locus and compound locus?

For definitions, search Google or Wikipedia or Yahoo.

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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. - January 23rd 2007, 02:32 AMsymmetryok
A locus could be a line, an equation, etc?

- January 23rd 2007, 03:36 AMticbol
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,..... - January 23rd 2007, 05:22 PMsymmetryok
Okay...I will study locus more deeply.