In this essay, conic sections in taxi geometry will be studied. The area of ​​mathematics used is geometry. I chose this topic because it seemed interesting to me. I had never heard of this topic before, but then our math teacher introduced us to a math web page and taxi geometry was one of the topics discussed there. I've looked into the topic before and found issues that seemed interesting to explore. I started with a basic example, just to compare Euclidean and taxi distance, after which I went further into the world of taxi geometry. I explored the conic sections (circle, ellipse, parabola and hyperbola) of taxi geometry. All images, except figure 12, were drawn by me in the program called Geogebra. PROBLEM DEFINITION The problem given by the teacher was: A probe on the surface of the planet Mars has a limited amount of fuel left. Due to the broken rudder it can only move from north to south and from east to west. What points can he achieve if he has to return to his base? I solved the problem by then finding the shape of a circle in the so-called taxi geometry. My research question was: How would other conic sections appear in taxi geometry? INTRODUCTION TO TAXICAB AND THE EUCLIDEAN DISTANCE I believe it is my duty to define the two distances that the essay will talk about: Euclidean distance and taxi distance, since many people, besides me, have probably never heard of taxi distance. EUCLIDEAN DISTANCE The Euclidean distance was proposed by the Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, expressed as the length of a line segment and is given by the Pythagorean theorem. The Euclidean distance formula is a square...... middle of paper...... (2014) Characteristic column of the AMS. [online] Available from: http://www.ams.org/samplings/feature-column/fcarc-taxi [Accessed: 02/03/14].P. Thompson, K. (2010) Taxi Geometry - General Information. [online] Available from: http://www.taxicabgeometry.net/general/index.html [Accessed 02/03/14].RAKANOVIČ, A. and ŠURC, D. and MITROVIČ, B. (2007) Stožnice v taksi razdalji.WIKIPEDIA. (2014) Conic section. [online] Available from: http://en.wikipedia.org/wiki/Conic_section. [Accessed 02/03/14].COMPONENT, C. (2007) Taxicab Geometry: Not the Shortest Ride Across Town. Iowa: Iowa State University.BUCHANAN, L. et al. (2012) Standard Level Mathematics. Oxford: Oxford UniversityImage:PBROKS13 (2009) The three conic sections that are created when a double cone is intersected with a plane. [image] Available from: http://en.wikipedia.org/wiki/File:Conic_sections_with_plane.svg