### Review of Equations of Straight Lines

The equation of the line parallel to x-axis is x = a When a = 0, x = 0 will be the equation of y-axis. In the same way, the equation of the line parallel to y-axis is y = b. If b = 0 , then y = 0 will be the equation of the x-axis.

**Three standard forms of equation of a line**

Three standard forms of equation of a line are given below:

- y = mx + c, is known as the slope-intercept form where m and c are the slope and the y- intercept respectively.
- x/a + y/b = 1, is known as the double-intercept form where a and b are the x-intercept and y- b intercept respectively.
- xcosα + ysinα = p is known as the normal form or perpendicular form where p is the perpendicular from origin to the line and a, the angle made by the perpendicular with x- axis.

**Equations of lines in spacial cases:**

The following are the two special forms of a line:

**Point slope form:**y – y₁ = m(x – x₁) where m is the slope of the line through (x₁, y₁).**Two points form:**y – y₁ = {(y₂ – y₁) / (x₂ – x₁)} (x – x₁) is the line through two given points (x₁, y₁) and (x₂,y₂)

### Linear Equation

The general equation of first degree in x and y is Ax + By + C = 0 where A, B and C constants and A, B are not simultaneously zero. This equation is called the linear equation. This equation always represents a straight line

### Important Points of Concurrencies

The following are the four important definitions of point of concurrencies of three straight lines.

**i) Orthocentre: **The perpendiculars drawn from the vertices on their opposite sides meet at a point. This point is known as ‘Orthocentre’.

**ii) Circumcentre: **The perpendicular bisectors of the sides of a triangle meet at a point. This point is known as ‘circumcentre’.

**iii) Incentre: **The bisectors of the internal angles of a triangle meet at a point. This point is known as ‘Incentre’. iv) Centroid: The medians of a triangle meet at a point. This point is known as ‘centroid’.

### The Two Sides of a Line

Let P (x,y,) and Q(x, y) be any two points and Ax+By+C=0 a line.

Join PQ. Let PQ (produced if necessary) meet the given line at R. Let PR:RQ=mn, m:n is positive if R divides PQ internally i.e. P and Q are on opposite sides of the line (Fig (a)); and m:n is negative if R divides PQ externally, i.e. P and Q are on the same sides of the line (Fig. (b)).