. Introduction Analytical Geometry of two dimension is used to describe geometric objects such as point, line, circle, parabola, ellipse, and hyperbola using Cartesian coordinate system . Two thousand years ago (≈ - BC (BCE)), the ancient Greeks studied conic curves, because studying them elicited ideas that were exciting, challenging, and interesting. They could not have imagined the applications of these curves in the later centuries.
Solving problems by the method of Analytical Geometry was systematically developed in the first half of the th century majorly, by Descartes and also by other great mathematicians like Fermat, Kepler, Newton, Euler, Leibniz, l’Hôpital, Clairaut, Cramer, and the Jacobis. Analytic Geometry grew out of need for establishing algebraic techniques for solving geometrical problems and the development in this area has conquered industry, medicine, and scientific research. The theory of Planetary motions developed by Johannes Kepler, the German mathematician cum physicist stating that all the planets in the solar system including the earth are moving in elliptical orbits with Sun at one of a foci, governed by inverse square law paved way to established work in Euclidean geometry. Euler applied the co-ordinate method in a systematic study of space curves and surfaces, which was further developed by Albert Einstein in his theory of relativity.
Applications in various fields encompassing gears , vents in dams, wheels and circular geometry leading to trigonometry as application based on properties of circles; arches, dish, solar cookers , head-lights , suspension bridges, and search lights as application based on properties of parabola; arches, Lithotripsy in the field of Medicine, whispering galleries, Ne-de-yag lasers and gears as application based on properties of ellipse; and telescopes, cooling towers, spotting locations of ships or aircrafts as application based on properties of hyperbola, to name a few. Fig. . Fig.
. Fig. . René Descartes – - - Two Dimensional Analytical Geometry - II Fig.
. Fig. . A driver took the job of delivering a truck of books ordered on line.
The truck is of m wide and . m high, while driving he noticed a sign at the semielliptical entrance of a tunnel; Caution! Tunnel is of m high at the centre peak. Then he saw another sign; Caution!
Tunnel is of m wide. Will his truck pass through the opening of tunnel’s archway? We will be able to answer this question at the end of this chapter.