Question 1169058: a point moves so that the difference between its distance from (3,0) and (-3,0) is 4. find the equation of its locus
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
This is the definition of a hyperbola with foci at (3,0) and (-3,0); that means the center is at (0,0), and the major axis is horizontal. The general equation is
In that equation, a is the semi-major axis (distance from the center to each vertex) and b is the semi-minor axis.
a and b are related by the equation
where c is the distance from the center to each focus.
In this example, then, we know c=3.
It is easy to find the two points on the x-axis that are on the graph and are therefore the vertices. With a distance of 6 between the two vertices, and a difference of 4 between the distances of a point from the two vertices, the vertices are at (2,0) and (-2,0); that makes a=2 and a^2=4.
Then using  , we find  .
So the equation of the locus is
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