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
• B. a straight line
• C. a hyperbola
• D. an ellipse

Answer 1

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 $d_1$ and $d_2$ bet the distances from the foci to the point, then$|d_1-d_2|=2a$.

Hence, option C is correct.