What is Statistics? It is a branch of mathematics. It involves collection, analysis, interpretation, presentation, and organization of data. (Dictionary Definition). Descriptive Statistics summarizes the data with the help of few indices, such as mean (the central tendency) and standard deviation (the dispersion). Inferential Statistics draws conclusions from data that are subject to random variation.… Continue reading Statistics, Correlation and Regression

# Category: XI

## Set Theory

Introduction The set theory, developed by George Cantor, forms a basis for advanced mathematical topics, such as the calculus, real and complex analysis etc. It defines functions, which are an extremely important entity in mathematics. Definition A set is a collection of well defined objects. For example, the set of all subjects studied by… Continue reading Set Theory

## Sequences and Series

We use the words sequence and series interchangeably and we generally mean a continuation of numbers/events by them. In mathematics, however, these words have a particular meaning. A sequence (also known as progression) is an arrangement of numbers in a specific order, in such a way that a definite relation exists between the numbers and… Continue reading Sequences and Series

## Hyperbola

NOTE: We are going to use the section formula to derive the equation of hyperbola, as we did for ellipse. Since there are 2 variants of the formula (external and internal division), we get 2 foci and 2 directrices. A hyperbola is a conic section, whose eccentricity $latex {e}&s=1$ is greater than 1. In other… Continue reading Hyperbola

## Ellipse

NOTE: We are going to use the section formula to derive the equation of ellipse. Since there are 2 variants of the formula (external and internal division), we get 2 foci and 2 directrices. An ellipse is a conic section, whose eccentricity $latex {e}&s=1$ is less than 1. In other words, if $latex {S(ae,0)}&s=1$ is… Continue reading Ellipse

## Parabola

The word parabola originated as a combination of 2 Greek words, para, which means besides and bole, which means throw. When any heavy object is thrown in air, its trajectory is a parabola. Hence the name. The eccentricity of parabola, $latex {e}&s=1$ is $latex {1}&s=1$. Let $latex {S(a,0)}&s=1$ be the focus and $latex {d \equiv x+a=0}&s=1$… Continue reading Parabola

## Focus-Directrix Property of Conic Sections

To get the equation of a conic in terms of $latex {x}&s=1$ and $latex {y}&s=1$, we use a property, known as the focus-directrix property. Let there be a fixed line $latex {l}&s=1$ (The Directrix) and a fixed point $latex {S}&s=1$ (The Focus). Let $latex {P}&s=1$ be a point on the locus of conic and let… Continue reading Focus-Directrix Property of Conic Sections