An ellipse is a type of conic section, which is a curve formed by a plane intersecting a double cone. Conic sections include ellipses, circles, parabolas, and hyperbolas. While the other conic sections have specific characteristics and equations, we will focus on ellipses in this article.

The equation of an ellipse in standard form is (x - h)^2 / a^2 + (y - k)^2 / b^2 = 1, where (h, k) represents the center of the ellipse, 'a' is the length of the semi-major axis, and 'b' is the length of the semi-minor axis. By manipulating the parameters a and b, we can manipulate the shape and orientation of the ellipse.

For example, when a = b, the ellipse becomes a circle. As a decreases relative to b, the ellipse becomes elongated vertically, and as a increases relative to b, the ellipse becomes elongated horizontally.

Understanding the relationship between ellipses and conic sections is not only fascinating but also has practical applications in various fields such as astronomy, engineering, and architecture.