What are we learning ?

Competency in Focus: Coordinate Geometry

This problem from B.Stat. (Hons.) based on coordinate geometry Admission Test 2005 – Objective Problem 5  is based nature of curve.

First look at the knowledge graph:-

calculation of  mean and median- AMC 8 2013 Problem

Next understand the problem

The equation $x(x+3)=y(y-1)-2$ represents
(A) a hyperbola

(B) a pair of straight lines
(C) a point

(D) none of the foregoing curves

Source of the problem

B.Stat. (Hons.) Admission Test 2005 – Objective problem 5

Key Competency

Coordinate Geometry

Difficulty Level
Suggested Book

Start with hints 

Do you really need a hint? Try it first!
It cannot be a stright line becouse Stright line are linear equation of the form. \(ax+by+c=0\).
So it may be a circle or a point if radius is zero, But when we generilsed it to the stanard form of circle we get negetive radius. so it cant be either of this one. Hint: Stanrd form of circle is $(x-h)^{2}+(y-k)^{2}=r^{2}$.
Now lets Try to factorize to find the prouct of two linear equations so as we can vberify the pair of straight line. $a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c=0$
This equation represents two straight lines, if $\Delta=a b c+2 f g h-a t^{2}-b g^{2}-c h^{2}=0$
or $\left|\begin{array}{lll}{a} & {h} & {g} \\ {h} & {b} & {f} \\ {g} & {f} & {c}\end{array}\right|=0$.

I.S.I. & C.M.I. Program

Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are: B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.
The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.

Learn more
Mathematics of How Virus can Grow

The Mathematics of How Virus can Grow

The Mathematics of How Corona Virus Grow? The beautiful tale of undeterministic mathematics of chance and chaos of when they will become extinct or when they will thrive.

The Exaggerated Triangle Inequality

Triangle Inequality is an exaggerated version of the Basic Idea of the Euclidean Plane. Let’s do some Triangle inequality Problems and Solutions.

geometric median

Geometric Median |Understand the concept

Geometric Median is an important concept in the intersection of Geometry, Data Analysis and Algorithms. This article explores the concept.

examples and counterexamples - build your own examples

Examples & Counterexamples – A Way to Build Your Own Mathematics

This is an interesting article on how to build your own Mathematics with the help of examples and counter examples. Stay tuned.

Sets and Venn diagrams |B.Math Entrance

Try this beautiful problem from B.Math Entrance Exam based on sets and venn diagrams. You may use sequential hints to solve the problem.

INMO 2007

Try to solve these interesting INMO 2007 Questions. Solve them and write the answers in the comment to check your answers.

Order of General and Special Linear Group

Here is the post in which you would learn about the Order of General and Special Linear Group with the help of a problem. Try it and learn the solution.

Maximizing Arrangements

Here is a post related to a problem based on maximizing arrangements in Mathematics. Try the problem and learn the solution.

Gaps in Permutation | TOMATO Objective Problem

The simplest example of power mean inequality is the arithmetic mean – geometric mean inequality. Learn in this self-learning module for math olympiad

Geometry of Tangents | ISI Entrance B.Stat 2009

Objective Problem Geometry (ISI Entrance) Find the radius of smaller circle. 01$\frac{3}{4}$2 Key Concepts 2D Geometry Similar Triangles Linear Equations Check the Answer Answer: $\frac{3}{4}$ ISI Entrance B.Stat Objective Problem, India Test of Mathematics at 10+2...