Draw two points on the drawing pad using the ‘New Point’ tool. Use the ‘Slider’ tool and define two sliders, say d and r.
Use the “Circle with centre and radius’ tool and draw a circle with A as the centre and r as the radius. Draw another circle with B as the centre and d -r as the radius. Use the intersect tool and find the intersection points of these two circles. Right click of these points and put their trace on.
Animate the slider by right clicking on that particular slider and putting on the animation.

Try out different ways to make hyperbola using GeoGebra.