## Distance Formula

November 1st, 2006 . by Vanaja## History of Analytical Geometry

October 13th, 2006 . by VanajaWe know Geometry is one of the most ancient branches of mathematics. The big step forward in geometry after the Greeks, was the development of a new method called Co-ordinate geometry or Analytical geometry. Modern analytical geometry is also called “Cartesian” after the name of Rene Decartes (1596-1665). But the fundamental principles and methods were already discovered by Pierre de Fermat(1601-1665). Unfortunately, Fermats treatise on the subject entitled “*Ad locus planos et so lidos Isagoge*“(Introduction to plane and solid loci) was published only published posthumously in 1679. So Decartes came to be regarded as the unique inventor of the analytical geometry.

In co-ordinate geometry, we enlist the services of Algebra in aid of Geometry.

## Locus -Definition

July 23rd, 2006 . by Vanaja**Locus:** When a point moves subject to certain specified conditions, the path traced out by it is called locus.

**Equation of a locus:** Equation to a locus is the algebraic relation that exists between x and y coordinates of a general point on the locus.**Example:**

Find the equation of the locus of points such that the sum of its distances from (0,3) and (0,-3) is 8.

**Solution: ***(To solve this problem you must know ***Distance Formula***)*Let P(x,y) be any point of the locus and A and B be the points (0,3) and

(0,-3) respectively.