Maths.CLIL definizioni e teoremi, le coniche

Conics (le coniche) maths.CLIL

Learn the basics

Conic sections (or simply conics) are curves obtained as the intersection of the surface of a cone with a plane, called a cutting plane. There are three different types of conics: the hyperbola, the parabola, and the ellipse. The circle is also a conic: it is a special case of an ellipse.

Conics as loci of points

Given a point F called the focus and a line d called the directrix, a conic is the set (called locus) of all points P such that the ratio of the length PF to the distance of P from d is constantly equal to e ∈ ℝ₊ (the eccentricity). Depending on the value of e we have:

• e = 0: a circle
• 0 < e < 1: an ellipse (e = 0 would be a circle)
• e = 1: a parabola
• e > 1: a hyperbola

General equation of a conic

Every conic is represented by an equation in the form Ax² + Bxy + Cy² + Dx + Ey + F = 0, with A, B, C, D, E, and F real numbers and A, B, C not all zero. Conversely, we can recognize a conic in the Cartesian plane by arriving at a non-empty set of real solutions for a second degree algebraic equation in two variables.