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About LinkBacks(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?Originally Posted by symmetry
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.
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,.....
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