### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Some various forms of the equation of a line

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(i) If a line is at a distance and parallel to -axis, then the equation of the line is .

(ii) If a line is parallel to -axis at a distance from -axis, the the equation of the lines is

The position of points is relative to a given line:

Let and two given points .

(i) The two points are on the same side of the straight line   if, and   have the same sign.

(ii) The two points are on the opposite sides of the line , if    and have opposite sign.

Equation of bisectors of the angle between to intersecting line:

Equation of bisectors and are

Bisectors of the angle containing a given point (h , k) its interior:

Let the equation of two-line   and be given by

To obtain the equation of the bisector of the angle containing in its interior, proceed as follows:

(1) First see if  and   have the same or opposite signs.

(i) If they have the same sign, write

(ii) If they have the opposite sign, write

(2) Write the bisector of the angle containing in its interiro as:

Note:

Bisector of the angle, not containing in its interior, is given by ,

Provided  and have the same sign.

Pair of Straight Lines:

Consider the equation which is a second degree homogenous equation in and , can be written as which is  quadratic  in . This gives   or   which represents a pair of straight lines,  with slopes

Change of Axes (Shifting of Origin)

Let the origin is shifted to a point . If are coordinates of a point referred to old axes and are the coordinates of the same points referred to new axes, then

Images of a point with respect to a line:

Let the image of a point with respect to   be , then

(i) The image of the point wrto -axis is

(ii) The image wrto -axis is .

(iii) The image of the point wrto mirror   is .

(iv) The image of wrto the line mirror is

(v) The image of wrto origin is

(vi) The length of perpendicular from a point to a line is

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