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 webpage and taxi geometry was one of the topics covered. I've looked at the topic before and came across some issues that seemed interesting to explore. I started with a basic example, just to compare Euclidean and taxi distance, and then moved 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 posed by the professor was as follows: A probe on the surface of the planet Mars has a limited amount of fuel. Due to a broken rudder, he can only move north to south and east to west. What points can he reach if he has to return to his base? I solved the problem and thus found a circle shape in what is called taxi geometry. My research question was: what would other conic sections look like in taxi geometry? PRESENTATION OF TAXICAB AND EUCLIDEAN DISTANCE I think it is my duty to define the two distances that the essay is going to talk about: the Euclidean distance and the taxi distance, as many people as I have probably never heard of the distance by taxi.EUCLIDEAN DISTANCEThe Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, represented by the length of a line segment and given by the Pythagorean theorem. The formula for Euclidean distance is a square...... middle of paper ...... (2014) AMS Feature Column. [online] Available at: http://www.ams.org/samplings/feature-column/fcarc-taxi [Accessed: 02/03/14].P. Thompson, K. (2010) Taxi Geometry – General Information. [online] Available at: 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 at: http://en.wikipedia.org/wiki/Conic_section. [Accessed 02/03/14].COMPONENT, C. (2007) Taxi geometry: not the shortest route across the city. Iowa: Iowa State University. BUCHANAN, L. Et al. (2012) Standard Level Mathematics. Oxford: University of OxfordImage: PBROKS13 (2009) The three conic sections created when a double cone is intersected by a plane. [image] Available at: http://en.wikipedia.org/wiki/File:Conic_sections_with_plane.svg