## 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 $$O$$,… 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 $$X$$ and $$Y$$ axes new coordinate axes are chosen parallel to the given… Click here to read more

Let the $$xy$$-coordinate system be rotated through an angle $$\theta $$, such that the range of the angle is $$0… Click here to read more

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

Let $$P\left( {{x_1},{y_1}} \right)$$ and $$Q\left( {{x_2},{y_2}} \right)$$ be any two points on the given line $$l$$. Also let $$\alpha $$… Click here to read more

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

Consider the straight line $$l$$. Let $$P\left( {x,y} \right)$$ be any point on the given line $$l$$. Suppose that $$\alpha… Click here to read more

Consider the straight line $$l$$ and let $$\alpha $$ be the inclination of the straight line as shown in the… Click here to read more

Let $$\alpha $$ be the inclination of the straight line $$l$$ as shown in the given diagram. Let $$P\left( {x,y}… Click here to read more

If $$\alpha $$ is the incrimination of a straight line $$l$$ passing through the point $$Q\left( {{x_1},{y_1}} \right)$$ then its… Click here to read more

The equation of a non-vertical line passing through two points $$A\left( {{x_1},{y_1}} \right)$$ and $$B\left( {{x_2},{y_2}} \right)$$ is given by… 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 $$a$$ and $$b$$ are non-zero $$X$$ and $$Y$$ intercepts of a line $$l$$, then its equation is of the… Click here to read more

If $$p$$ is the length of a perpendicular from origin to the non-vertical line $$l$$ and $$\alpha $$ is the… 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 $$l$$ is the straight line which is passing through the… Click here to read more

The general equation or standard equation of a straight line is given by \[ax + by + c = 0\]… Click here to read more

The general equation or standard equation of a straight line is: \[ax + by + c = 0\] In which, $$a$$… Click here to read more

The general equation or standard equation of a straight line is: \[ax + by + c = 0\] Where $$a$$… Click here to read more

The general equation or standard equation of a straight line is given by \[ax + by + c = 0\,\,\,\,{\text{… Click here to read more

The distance $$d$$ of the point $$A\left( {{x_1},{y_1}} \right)$$ from the line $$ax + by + c = 0$$ is… 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 $$A\left( {{x_1},{y_1}} \right)$$, $$B\left( {{x_2},{y_2}} \right)$$ and $$C\left( {{x_3},{y_3}} \right)$$ be the vertices of the triangular region as shown… Click here to read more

The point of intersection of two lines $${a_1}x + {b_1}y + {c_1} = 0$$ and $${a_2}x + {b_2}y + {c_2}… Click here to read more

The conditions of concurrency of three lines $${a_1}x + {b_1}y + {c_1} = 0$$, $${a_2}x + {b_2}y + {c_2} =… Click here to read more

Let $${l_1}$$ and $${l_2}$$ be two coplanar and non-parallel lines with inclination $${\alpha _1}$$ and $${\alpha _2}$$ respectively, as shown… Click here to read more

Here we prove that the altitudes of a triangle are concurrent. Let $$A\left( {{x_1},{y_1}} \right)$$, $$B\left( {{x_2},{y_2}} \right)$$ and $$C\left( {{x_3},{y_3}}… Click here to read more

Here we prove that the right bisectors of a triangle are concurrent. Let $$A\left( {{x_1},{y_1}} \right)$$, $$B\left( {{x_2},{y_2}} \right)$$ and $$C\left(… Click here to read more

Consider the two straight lines \[\begin{gathered} {a_1}x + {b_1}y + {c_1} = 0\,\,\,\,\,{\text{ – – – }}\left( {\text{i}} \right) \\… Click here to read more

Let $$A\left( {{x_1},{y_1}} \right)$$ and $$B\left( {{x_2},{y_2}} \right)$$ be the ends of a segment, then the slope $${m_1}$$ of the… 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 \[a{x^2} + 2hxy + b{y^2} + 2gx +… Click here to read more

As we know that the equation of the form $$a{x^2} + 2hxy + b{y^2} = 0$$ is called the second… Click here to read more

In previous tutorials, we saw that the equation of the form $$a{x^2} + 2hxy + b{y^2} = 0$$ is called the… Click here to read more

Find the lines represented by the second degree homogeneous equation $$3{x^2} + 7xy + 2{y^2} = 0$$. Also find the… 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 $$P\left( {{x_1},{y_1}} \right)$$ and $$Q\left( {{x_2},{y_2}} \right)$$ be any two points on the line. We will find the distance between… Click here to read more

Let $${\text{P}}\left( {{{\text{x}}_1},{{\text{y}}_1}} \right)$$ and $${\text{Q}}\left( {{{\text{x}}_2},{{\text{y}}_2}} \right)$$ be any two points on the line. Let a point $${\text{R}}\left( {{\text{x}},{\text{y}}}… Click here to read more