SOLUTION: a point moves so that the difference between its distance from (3,0) and (-3,0) is 4. find the equation of its locus

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(13200) (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

RELATED QUESTIONS
Find the equation of the locus of a point which moves such that its distance from (-3, 0) (answered by josgarithmetic)

Find the equation of the locus of a point which moves so that its distance from the point (answered by richwmiller)

Find the equation of the locus of a point which moves so that its distance from the... (answered by richwmiller)

Find the locus of point if point moves in such way that the difference of its distance... (answered by ikleyn)

PLEASE HELP. A POINT MOVES SO THAT ITS DISTANCE FROM THE LINE {{{ x-16=0 }}} IS ALWAYS... (answered by josgarithmetic)

Derive the equation of the locus of a point P(x,y) which moves so that its distance from... (answered by josgarithmetic,ikleyn,greenestamps)

What is the equation of the locus of the point which moves so that its distance from... (answered by ikleyn)

Find the equation of the locus of a point which moves so that its distance from the point (answered by richwmiller,KMST)

Find the equation of the locus of a point which moves so that its distance from the point (answered by josgarithmetic,ikleyn)