A classification of a conic through three no colinear given points, according the position of its center. Nine point ellipse.
In this note we study the maximal inscribed and the minimal circumscribed ellipse of a cenrally symmetrc convex figure F and we prove two theorems between the area and the remarcable elements of the figure.
The convex figure K has conjugate diameters if and only if its symmetroid K* is an affine image of a Radon curve
For the triangle T of a minimum perimeter circumscribed to a convex figure (c) the excircles of T are tangent to (c).
Let Q(z)=z3+a1z2+a2z+a3=0 be a cybic in C and z1,z2,z3 the roots denoted in the plane by the points A,B,C. The Steiner ellipse in the triangle ABC is denoted by E and F1, F2 the foci. Van den Berg’s theorem asserts that the roots of the derivate Q'(z) are the complex numbers defined in C by the points F1 and F2.