The general form of a conic section is given by the equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.
The different types of conic sections are circle, ellipse, parabola, and hyperbola. They are determined by the values of A, B, and C in the general form equation.
The shape of a conic section can be determined by the values of A, B, and C in the general form equation. A circle has A = C and B = 0, an ellipse has A and C with the same sign, a parabola has A = 0, and a hyperbola has A and C with opposite signs.
The focus-directrix property states that for any point on a conic section, the distance from the point to the focus is equal to the distance from the point to the directrix. This property is true for all types of conic sections.
Conic sections have many real-life applications. For example, the shape of a satellite's orbit around the Earth is an ellipse, and the shape of a satellite dish is a parabola. Conic sections are also used in optics, such as in the design of lenses and mirrors.