## 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 given and axes, new coordinate axes are chosen parallel to the given ones, we say... 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: Angle from X-axis to any given non horizontal line is called inclination of line . Here... Click here to read more

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

When represents the straight line graphically the two main attributes of will come out, one is the -intercept and the... Click here to read more

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

Consider the straight line and be the inclination of the straight line as shown in the given diagram now the... 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 straight line is Now... 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 Dollars 3.15 per liter and 800 liters of milk... Click here to read more

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

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

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

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

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

The general equation or standard equation of a straight line is given by Where and are any constants and also... Click here to read more

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

The distance of the point from the line is given by Let be the inclination of the line as show... 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 proof this formula we have the... Click here to read more

The conditions of concurrency of three lines , and is given by Where . To proof 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

The altitudes of a triangle are concurrent. Let , and be the vertices of the triangle . If is the... Click here to read more

The right bisectors of a triangle are concurrent. Let , and be the vertices of the triangle . Let ,... Click here to read more

Consider the two straight lines For any nonzero constant , the equation of the form being linear in and ,... 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 altitude of a triangle we examine the following example, consider the triangle having vertices ,... Click here to read more

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

In this tutorial we shall represent equations of straight lines into matrix form; first we will discuss one linear equation... Click here to read more

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

General Equation of Second Degree: The equation of the form Where , and are not simultaneous zero, is called the... 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

We studied in previous tutorials that the equation of the form is called the second degree homogeneous equation. And we... Click here to read more

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

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

Let and are any two points on the line. We 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