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Question

The locus of a point that moves such that the difference of its distance from two fixed points is always a constant, is


A

a circle

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B

a straight line

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C

a hyperbola

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D

an ellipse

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Solution

The correct option is C

a hyperbola


Explanation of correct option:

Hyperbola is "the set of all points in a plane such that the difference of the distances from two fixed points (foci) is constant".

The difference of the distances to any point on the hyperbola(x,y) from the two foci (c,0)and(-c,0) is a constant. That constant will be 2a.

If we let d1 and d2 bet the distances from the foci to the point, then|d1d2|=2a.

Hence, option C is correct.


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