# Math

## Circle : Introduction

Definition : Circle : it is the locus of a point that in which moves in a plane such that its distance from a fixed point in a plane is always constant. The fixed point is known as centre and the constant distance is known as radius of the circle. Equation of circle— According to …

## Introduction of Pair of straight lines

Pair of Straight lines :   It is combined product of more than one straight lines. Let us assume — For two lines : L1 :::      ax + by + c = 0  ….(1) L2 :::     a1x + b1y + c1 = 0.  ….(2) Hence  (ax + by + c)( a1x …

## Rotation axes and shifting origin

Change of Axis : Rotation in axes and shifting in origin. 1.Shifting of origin without Rotation of Axes : Initial :             Origin =  O( 0 , 0)            X-axis  = OX            Y-axis  = OY               …

## Mirror property in a straight line

Mirror property in a straight line : Reflection in the surface — Incident ray (IP) Normal (PN) Reflected ray (PR) Angle of incidence = angle of reflection Refraction in the surface — Let assume Incident ray makes an angle θ  with tangent then refracted ray makes an angle (θ + a ) with tangent. Where a  is …

## Properties of a straight line

Properties of a straight line – Let equation ax + by + c = 0 1.Method to Write a line parallel to a given line – Change only the constant term in the given equation, the term of x and y remaining unchanged. The changed constant will be found by an additional given condition. For …

## Angle Between Two Lines

Angle between two lines : Let two line y = m₁x + c₁  and  y = m₂x + c₂  and intersect at point A and makes an angle θ. Where m₁ = tana and m₂ = tanβ, then angle between two lines is – θ = a  – β   If m₁  = m₂ Both lines are parallel …

## Position of points with respect to line :

Position of points with respect to line : Let Equation of a straight line –ax + by + c = 0 And points P(x₁ ,y₁) and Q(x₂ , y₂) , then find position of points with respect to line- Assume, the line PQ intersection point L at A(x, y) and let A divides PQ in …

## equation of straight lines

Equation of  straight lines : 1.General form The first-degree equation in x and y is known as a general form of a straight line. Example –  ax + by + c = 0 , where  a and b are not both zero at a same time. x = 0 , Y-axis. y = 0 , …

## the slope of a straight line

Slope of a line : The Slope of a straight line is defined as that it is described direction and as well as steepness of a line. Or The Slope of a line can be defined as that it is changing rate of y with respect to x in x-y plane. Notation : Generally slope …

## Quadrilaterals shape & its properties

Quadrilaterals Quadrilaterals shape & its properties Quadrilateral : A quadrilateral is closed 2-Dimensional shape whose covered with four sides- Rectangle. Square. Rhombus. Paralellogram. Quadrilaterals shape & its properties 1.Rectangle: A Quadrilateral with four sides that in which opposite sides are parallel and equal to each other and also this shape contained four right angles. So, …

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