91Ó°ÊÓ

Answer: The eccentricity (e) is a value that determines the shape of a conic section, and it is connected to the foci of the conic. It affects the shape of each type of conic section as follows: 1. e = 0: Circle - The foci coincide at the center, and the distance from any point on the circle to the center is constant. 2. 0 < e < 1: Ellipse - The ellipse's shape becomes more elongated as the eccentricity increases, with the foci approaching the ends of the major axis and a constant total distance from any point on the ellipse to both focal points. 3. e = 1: Parabola - The conic section becomes unbounded, with only one focus and equal distance from any point on the parabolic curve to the focus and a line called the directrix. 4. e > 1: Hyperbola - The conic section becomes two distinct unbounded branches, with two foci and a relationship involving the difference of distances from each focus to points on the two branches, and the shape becomes more elongated as the eccentricity increases.