GEOMETRIC PROPERTIES OF SOME ALGEBRAIC CURVES SZIL ´ ARD ANDR ´ AS, ´ ARP ´ AD BARICZ Abstract. In this note we study a few classes of curves with interesting geometric properties. The definition of these classes were suggested by geometric properties of some well known curves like: straight strophoid, cissoid, the curve defined by V. Schultz and L.C. Strasznicki which con- tains both the cissoid and strophoid. Definition 1.1. The curve γ is called an L−type curve if admits a para- metric representation of the form (1.1)  x = f 1 (t) g(t) y = f 2 (t) g(t) where the coefficients of the functions f i (t)= a i t 3 + b i t 2 + c i t + d i ,i ∈{1, 2}, g(t)= a 3 t 3 + b 3 t 2 + c 3 t + d 3 satisfy the following condition b 1 = b 2 = b 3 =0 or c 1 = c 2 = c 3 =0. Definition 1.2. The curve γ is called a C −type curve if admits a parametric representation of the form (1.2)  x = f 1 (t) g(t) y = f 2 (t) g(t) where the functions f i (t)= a i t 3 + b i t 2 + d i ,i ∈{1, 2},g(t)= b 3 t 2 + d 3 satisfy the following condition (1.3) ( f 2 1 + f 2 2 ) . . .g in R[X]. Remark 1.1. 1. It is obvious that any C −type curve is an L−type curve; 2. The straight cissoid defined by the equations x(t)= rt 2 1+t 2 and y(t)= rt 3 1+t 2 , where r> 0 is a C −type curve (the line x = r is the asymptote of the cissoid and r is the radius of the circle which generates the circle, see [1], [9], [3]). The curve defined by the relations x(t)= rt 2 t 3 +1 and y(t)= rt 3 t 3 +1 is an L−type curve but it is not a C −type curve. Notations. In what follows we denote an arbitrary point M (x, y) on the curve by M (m), which means x(m)= f 1 (m) g(m) ,y(m)= f 2 (m) g(m) , if in our 1