To construct a hyperbola, I first made a circle. Next, I created a point outside of the circle (D). Then, I placed a point on the circle (E) and made a line through that point and the center of the circle. I then connected E to D with a segment and created its perpendicular bisector. Finally, I made a point at the intersection of the perpendicular bisector and the other line (F). To sketch the hyperbola, trace point F and animate point E. You can also use the locus tool to create the hyperbola (first select F then E).
