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 …
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 …
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 : 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 – 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 : 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 : 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 : 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 , …
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 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, …