#TITLE_ALTERNATIVE#

• Main Author: MAULANA MUHAMMAD (NIM: 90112301), GUNTUR
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/22314
• Institution: Institut Teknologi Bandung

Circle is an object of geometry. Given a point O and a nonnegative real number r, the circle with center O and radius r is de&#64257;ned to be the set of all points P such that the distance from O to P is r. In algebra, we can write a circle as the following equation. Suppose C(X,Y ) = X2 + Y 2 + 2gX + 2fY + e = 0 with g2 + f2 &#8722; e &#8805; 0 and C0(X,Y ) = X2 + Y 2 + 2g0X + 2f0Y + e0 = 0 with g02 + f02 &#8722;e0 &#8805; 0 are two distinct circles. A circle can be produced from combination of two distinct circles with the expression &#955;C + µC0 = 0, for any &#955; and µ &#8712; R. Two basic circles C and C0 which are combined are called generator circles. <br /> <br /> There are three possibilities from the combination of two distinct circles: circle, line, or empty. The circles that are produced by two generators will have the same characteristic as with the generators’. The set of the circles forms a system of circle that is called pencil of circle. <br /> <br /> Based on two generators’ positions, there are three kinds of pencil of circles: hyperbolic pencil (two generators that do not intersect each other at any point), elliptic pencil (two generators that pass through each other in exactly two points), and parabolic pencil (two generators are tangent to each other at a single point). The three kinds of pencils are called hyperbolic pencil, elliptic pencil, and parabolic pencil because there is bundle of hyperbola, ellips or parabola in each of that pencil. <br />