## Introduction to Analytic Geometry

Geometry is one of the most ancient branches of mathematics, concerned with the properties of space and object – points,... Click here to read more

From basic to higher mathematics

Geometry is one of the most ancient branches of mathematics, concerned with the properties of space and object – points,... Click here to read more

Cartesian coordinates are defined through the use of two coordinate lines, one horizontal and the other vertical. Let their point of intersection be ,... Click here to read more

The medians of any triangle are concurrent and that the point of concurrency divides each one of them in the... Click here to read more

If in the plane with the given and axes new coordinate axes are chosen parallel to the given ones, we... Click here to read more

Let the -coordinate system be rotated through an angle , such that the range of the angle is about the... Click here to read more

Inclination of a Line: The angle from the X-axis to any given non horizontal line is called the inclination of line... Click here to read more

Let and be any two points on the given line . Also let be the inclination of the line as... Click here to read more

When a straight line is represented graphically the following two main attributes will come out: the -intercept and the -intercept of... Click here to read more

Consider the straight line . Let be any point on the given line . Suppose that is the inclination of the... Click here to read more

Consider the straight line and let be the inclination of the straight line as shown in the given diagram. Now... Click here to read more

Let be the inclination of the straight line as shown in the given diagram. Let be any point on the... Click here to read more

If is the incrimination of a straight line passing through the point then its equation of a straight line is... Click here to read more

The equation of a non-vertical line passing through two points and is given by To prove this equation let be... Click here to read more

Example 1: A milkman can sell 650 liters of milk at $3.15 per liter and 800 liters of milk at... Click here to read more

If and are non-zero and intercepts of a line , then its equation is of the form Since is an... Click here to read more

If is the length of a perpendicular from origin to the non-vertical line and is the inclination of , then... Click here to read more

Consider we have the given equation of a line, and this line is parallel to another line which passes through... Click here to read more

Consider that we have the given equation of a line, and this given line is perpendicular to another line which... Click here to read more

(i) Equation of a Line Parallel to the X-Axis: Consider that is the straight line which is passing through the point... Click here to read more

The general equation or standard equation of a straight line is given by In this case, and are constants and either... Click here to read more

The general equation or standard equation of a straight line is: In which, and are constants and either or .... Click here to read more

The general equation or standard equation of a straight line is: Where and are constants and either or . Convert... Click here to read more

The general equation or standard equation of a straight line is: Where and are constants and either or . Putting... Click here to read more

The general equation or standard equation of a straight line is given by Let be a point which does not... Click here to read more

The distance of the point from the line is given by Let be the inclination of the line as shown... Click here to read more

In order to find the distance between two parallel lines, first we find a point on one of the lines... Click here to read more

Let , and be the vertices of the triangular region as shown in the given diagram. Draw perpendiculars from the... Click here to read more

The point of intersection of two lines and is given by where . To prove this formula we have the given... Click here to read more

The conditions of concurrency of three lines , and is given by Where . To prove this formula we have... Click here to read more

Let and be two coplanar and non-parallel lines with inclination and respectively, as shown in the given diagram. The angle... Click here to read more

Here we prove that the altitudes of a triangle are concurrent. Let , and be the vertices of the triangle .... Click here to read more

Here we prove that the right bisectors of a triangle are concurrent. Let , and be the vertices of the triangle... Click here to read more

Consider the two straight lines For any nonzero constant , the equation of the form being linear in and is... Click here to read more

Let and be the ends of a segment, then the slope of the line joining and is The midpoint of... Click here to read more

To find the equation of the altitude of a triangle, we examine the following example: Consider the triangle having vertices... Click here to read more

To find the equation of the right bisector of a triangle we examine the following example: Consider the triangle having... Click here to read more

In this tutorial we shall convert equations of straight lines into matrix form. First we will discuss one linear equation in... Click here to read more

In this tutorial we shall discuss a system of three linear equations in matrix form. A System of Three Linear... Click here to read more

General Equation of the Second Degree The equation of the form is When , and are not simultaneously zero, is... Click here to read more

As we know that the equation of the form is called the second degree homogeneous equation, the second degree homogeneous... Click here to read more

In previous tutorials, we saw that the equation of the form is called the second degree homogeneous equation. And we know... Click here to read more

Find the lines represented by the second degree homogeneous equation . Also find the measure of the angle between them.... Click here to read more

To find the equation of the median of a triangle we examine the following example: Consider the triangle having vertices... Click here to read more

Let and be any two points on the line. We will find the distance between P and Q. For this, draw... Click here to read more

Let and be any two points on the line. Let a point be the point which divides PQ in the... Click here to read more