Statement 1 : A bullet is fired and it hits a target. An observer in the same plane heard two sounds: the crack of the rifle and the thud of the bullet striking the target at the same instant. Then the locus of the observer is a hyperbola where the velocity of sound is smaller than the velocity of the bullet. Statement 2 : If the difference of distances of a point $P$ from two fixed points is constant and less than the distance between the fixed points, then the locus of $P$ is a hyperbola.

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