# Math Blog

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### Intercepts on the Axes made by a Circle | Equation of the Circle | Examples

We will learn how to find the intercepts on the axes made by a circle. The lengths of intercepts made by the circle x^2 + y^2 + 2gx + 2fy + c = 0 with X and Y axes are 2$$\mathrm{\sqrt{g^{2} - c}}$$

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### Position of a Point with Respect to a Circle | Discuss the Positions of Points

We will learn how to find the position of a point with respect to a circle. A point (x1, y1) lies outside, on or inside a circle S = x^2 + y^2 + 2gx + 2fy + c = 0 according as S1 >= or <0, where S1 =

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### Equation of the Common Chord of Two Circles | Two Intersecting Circles

We will learn how to find the equation of the common chord of two circles. Let us assume that the equations of the two given intersecting circles be x2 + y2 + 2g1x + 2f1y + c1 = 0 and

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### Circle Through the Intersection of Two Circles | Family of Circles | Examples

We will learn how to find the equation of a circle through the intersection of two given circles The equation of a family of circles passing through the intersection of the circles

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### Circle Passing Through Three Given Points |Equation of a Circle|Solved Examples

We will learn how to find the equation of a circle passing through three given points. Let P (x1, y2), Q (x2, y2) and R (x3, y3) are the three given points. We have to find the equation of the circle

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### Equations of Concentric Circles | Circle having same Centre but different Radii

We will learn how to form the equation of concentric circles. Two circles or more than that are said to be concentric if they have the same centre but different radii.

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### Equation of a Circle when Line Segment Joining Two Given Points is a Diameter

We will learn how to find the equation of the circle for which the line segment joining two given points is a diameter. Let P (x1, y2) and Q (x2, y2) are the two given points on the circle

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### Circle Passes through the Origin and Centre Lies on y-axis |Equation of a Circle

We will learn how to find the equation of a circle passes through the origin and centre lies on y-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2

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### Circle Passes through the Origin and Centre Lies on x-axis |Equation of a Circle

We will learn how to find the equation of a circle passes through the origin and centre lies on x-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2

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### Centre of the Circle on y-axis | Equation of a Circle | Central form of Circle

We will learn how to find the equation when the centre of a circle on y-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2 = a^2. When the centre of a

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### Worksheet on Fundamental Concepts of Geometry | Basic GeometricalShapes

Practice the questions given in the worksheet on fundamental concepts of geometry. The questions are related to the basic geometrical shapes with which we are already familiar with.

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### Centre of the Circle on x-axis | Equation of a Circle | Central form of Circle

We will learn how to find the equation when the centre of a circle on x-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2 = a^2.

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### Circle Touches both x-axis and y-axis | Circle Touches both the Co-ordinate

We will learn how to find the equation of a circle touches both x-axis and y-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2 = a^2.

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### Circle Touches y-axis | Central form of the Equation of a Circle | Examples

We will learn how to find the equation of a circle touches y-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2 = a^2. When the circle touches y-axis

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### Circle Touches x-axis | Central Form of the Equation of a Circle touches x-axis

We will learn how to find the equation of a circle touches x-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2 = a^2. When the circle touches x-axis

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### General Equation of Second Degree Represents a Circle | Quadratic Equation

We will learn how the general equation of second degree represents a circle. General second degree equation in x and y is ax$$^{2}$$ + 2hxy + by$$^{2}$$ + 2gx + 2fy + C = 0

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### Circle Passes through the Origin |Equation of the Circle |Central form of Circle

We will learn how to form the equation of a circle passes through the origin. The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)^2 + (y - k)^2 = a^2

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### Parentheses | Examples using Parentheses | Brackets | Solved Examples

Parentheses are made like this ( ). They show what part we wish to work first in a number sentence. Some people call then brackets. 4 + 3 + 2 = 9 We can think of this as 7 + 2 = 9 or 4 + 5 = 9

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### Worksheet on Parentheses | Group the Numbers by using Parentheses

Practice the questions given in the worksheet on parentheses. Here we need to group the numbers by using parentheses and then add. 1. In the following number sentences first make 4s by

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### Centre of the Circle Coincides with the Origin |Centre Coincides with the Origin

We will learn how to form the equation of a circle when the centre of the circle coincides with the origin. The equation of a circle with centre at (h, k) and radius equal to a, is

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### General Form of the Equation of a Circle | Point Circle | Imaginary Circle

We will discuss about the general form of the equation of a circle. Prove that the equation x^2 + y^2 + 2gx + 2fy + c = 0 always represents a circle whose centre is (-g, -f) and radius

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### Equation of a Circle |Parametric Equations of the Circle| Point on Circumference

We will learn how to find the equation of a circle whose centre and radius are given. Case I: If the centre and radius of a circle be given, we can determine its equation: To find the equation

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### Definition of Circle | What is the Definition of Circle? | Radius of the circle

What is the definition of circle? A circle is defined as the locus of a point which moves in a plane such its distance from a fixed point in that plane is always constant.

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### Problems on Slope and Intercept | Intercepted between the Co-ordinate Axes

We will learn how to solve different type of problems on slope and intercept from the given equation. 1. Find the slope and y-intercept of the straight-line 5x - 3y + 15 = 0

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### Word Problems on Straight Lines | Straight Line Intersects the x-axis | Slope

Here we will solve different types of word problems on straight lines. 1. Find the equation of a straight line that has y-intercept 4 and is perpendicular to straight line joining (2, -3) and (4, 2).

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### Problems on Straight Lines | Straight Line Perpendicular to the Straight Line

We will learn how to solve different types of problems on straight lines. 1. Find the angle which the straight line perpendicular to the straight line √3x + y = 1, makes with the positive direction

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### Fundamental Concepts of Geometry | Line and Curves | Closed Curves

Geometry is one of the important part of mathematics. 1. Draw a straight path from Sam’s house to the school. 2. Draw a straight path from the factory to the hospital.

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### Points and Line Segment |Two Points in a Curved Surface|Line has Infinite Length

We will discuss here about points and line segment. We know when two lines meet we get a point. When two points on a plane surface are joined, a straight line segment is obtained.

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### General Form into Normal Form | Find the Perpendicular Distance from the Origin

We will learn the transformation of general form into normal form. To reduce the general equation Ax + By + C = 0 into normal form (x cos α + y sin α = p): We have the general equation Ax + By + C = 0

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### Concept of Fractions |Concept of Half|Concept of One Fourth|Concept of Two Third

Concept of fractions will help us to express different fractional parts of a whole. One-half When an article or a collection of objects is divided into two equal parts is called as half of the whole.

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### General Form into Intercept Form | Determine the Intercepts on the Axes

We will learn the transformation of general form into intercept form. To reduce the general equation Ax + By + C = 0 into intercept form (x/A + y/B = 1): We have the general equation Ax + By + C = 0.

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### General Form into Slope-intercept Form | Reduce the General Equation

We will learn the Transformation of general form into slope-intercept form. To reduce the general equation Ax + By + C = 0 into slope-intercept form (y = mx + b): We have the general equation

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### Multiplication Table Games | Math Multiplication Table | Multiplication Games

Multiplication table games are an interesting way for kids to learn math multiplication table. A fun way to practice times table by playing games. First the students need to learn

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### Bisector of the Angle which Contains the Origin | Equation of the Bisector

We will learn how to find the equation of the bisector of the angle which contains the origin. Algorithm to determine whether the origin lines in the obtuse angle or acute angle between the lines

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### Straight Line Formulae | Problems on Straight line in Co-ordinate Geometry

Straight line formulae will help us to solve different types of problems on straight line in co-ordinate geometry. 1. If a straight line makes an angle θ with the positive direction of the axis of x

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### Worksheet on Number in Expanded Form | Expanded Form | Standard Form

Practice the questions given in the worksheet on number in expanded form. Expanded form of a number is to break down each digit and write the number to show how each digit in the number represents

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### Equations of the Bisectors of the Angles between Two Straight Lines

We will learn how to find the co-ordinates of the point of intersection of two lines. Let the equations of two intersecting straight lines be a$$_{1}$$ x + b$$_{1}$$y + c$$_{1}$$ = 0

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### Worksheet on Basic Pattern | Completing the Series of Numbers | Basic Pattern

Practice the series of numbers given in the worksheet on basic pattern. The questions are based on completing the series of numbers to find the forward numbers and the number which is added to get

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### Concept of Pattern | Similar Patterns in Mathematics | Similar Pattern of Shape

Concept of pattern will help us to learn the basic number patterns and table patterns. Animals such as all cows, all lions, all dogs and all other animals have dissimilar features.

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### Distance of a Point from a Straight Line | Length of the Perpendicular

We will learn how to find the perpendicular distance of a point from a straight line. Prove that the length of the perpendicular from a point (x$$_{1}$$, y$$_{1}$$) to a line ax + by + c = 0 is

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### Number Words 100 to 1000 | Reading and Writing the Number in Words

We will learn how to read and write the numbers words 100 to 1000. Reading and writing the number in words from 100 to 199: Read one hundred five for 105 Read one hundred eighteen for 118

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### Position of a Point Relative to a Line | Position of a Point and a Straight Line

We will learn how to find the position of a point relative to a line and also the condition for two points to lie on the same or opposite side of a given straight line.

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### Identical Straight Lines | Slope-intercept form of a Line | Identical Lines

When the coefficients of two straight lines are proportional they are called identical straight lines. Let us assume, the straight lines a$$_{1}$$ x + b$$_{1}$$ y + c$$_{1}$$ = 0

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### Condition of Perpendicularity of Two Lines | Two Lines are Perpendicular

We will learn how to find the condition of perpendicularity of two lines. If two lines AB and CD of slopes m1 and m2 are perpendicular, then the angle between the lines θ is of 90°.

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### Equation of a Line Perpendicular to a Line | Slope of a Perpendicular Line

We will learn how to find the equation of a line perpendicular to a line. Prove that the equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + λ = 0, where λ is a constant.

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### Theorem on Properties of Triangle | p/sin P = q/sin Q = r/sin R = 2K

Proof the theorem on properties of triangle p/sin P = q/sin Q = r/sin R = 2K. Proof: Let O be the circum-centre and R the circum-radius of any triangle PQR. Let O be the circum-centre and R

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### Properties of Triangles | Semi-perimeter| Circum-circle|Circum-radius|In-radius

In trigonometry we will discuss about the different properties of triangles. We know any triangle has six parts, the three sides and the three angles are generally called the elements of the triangle.

### Tan Theta Equals 0 | General Solution of the Equation tan θ = 0 | tan θ = 0

How to find the general solution of the equation tan θ = 0? Prove that the general solution of tan θ = 0 is θ = nπ, n ∈ Z.

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### Cos Theta Equals 0 | General Solution of the Equation cos θ = 0 | cos θ = 0

How to find the general solution of the equation cos θ = 0? Prove that the general solution of cos θ = 0 is θ = (2n + 1) π/2, n ∈ Z

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