Ellipses and parabolas are both used to reflect and focus sound and light. So what is the real difference between an ellipse and a parabola? Do they reflect sound and light differently? If so, how are they different and what are the different applications? Some sources say that the parabola is halfway between an ellipse and a hyperbola. What does that mean? Is it really true? How does the gravitational slingshot work? Doesn't it violate the conservation of energy law? Is a parabola just half of a hyperbola, or half of an ellipse