Free Algebra
Miscellaneous Equations
Operations with Fractions
Undefined Rational Expressions
Writing Equations for Lines Using Sequences
Intersections of Lines and Conics
Graphing Linear Equations
Solving Equations with Log Terms and Other Terms
Quadratic Expresions - Complete Squares
Adding and Subtracting Fractions with Like Denominators
Multiplying a Fraction by a Whole Number
Solving Equations with Log Terms and Other Terms
Solving Quadratic Equations by Factoring
Locating the Solutions of the Quadratic Equation
Properties of Exponents
Solving Equations with Log Terms on Each Side
Graphs of Trigonometric Functions
Estimating Products and Quotients of Mixed Numbers
The circle
Adding Polynomials
Adding Fractions with Unlike Denominators
Factoring Polynomials
Linear Equations
Powers of Ten
Straight Lines
Dividing With Fractions
Multiplication Property of Equality
Rationalizing Denominators
Multiplying And Dividing Fractions
Distance Between Points on a Number Line
Solving Proportions Using Cross Multiplication
Using the Quadratic Formula
Scientific Notation
Imaginary Numbers
Values of Symbols for Which Fractions are Undefined
Graphing Equations in Three Variables
Writing Fractions as Decimals
Solving an Equation with Two Radical Terms
Solving Linear Systems of Equations by Elimination
Factoring Trinomials
Positive Rational Exponents
Adding and Subtracting Fractions
Negative Integer Exponents
Rise and Run
Multiplying Square Roots
Multiplying Polynomials
Solving Systems of Linear Inequalities
Multiplication Property of Radicals
A Quadratic within a Quadratic
Graphing a Linear Equation
Calculations with Hundreds and Thousands
Multiplication Property of Square and Cube  Roots
Solving Equations with One Log Term
The Cartesian Coordinate Plane
Equivalent Fractions
Adding and Subtracting Square Roots
Solving Systems of Equations
Exponent Laws
Solving Quadratic Equations
Factoring Trinomials
Solving a System of Three Linear Equations by Elimination
Factoring Expressions
Adding and Subtracting Fractions
The parabola
Computations with Scientific Notation
Quadratic Equations
Finding the Greatest Common Factor
Introduction to Fractions
Simplifying Radical Expressions Containing One Term
Polynomial Equations
Graphing and Intercepts
The Number Line
Adding and Subtracting Rational Expressions with Different Denominators
Scientific Notation vs Standard Notation
Factoring by Grouping
Extraneous Roots
Variables and Expressions
Linera Equations
Integers and Substitutions
Squares and Square Roots
Adding and Subtracting Rational Expressions with Different Denominators
Solving Linear Inequalities
Expansion of a Product of Binomials
Powers and Exponents
Finding The Greatest Common Factor
Quadratic Functions
The Intercepts of a Parabola
Solving Equations Containing Rational Expressions
Subtracting Polynomials
Solving Equations
Adding Fractions with Unlike Denominators
Solving Systems of Equations by Substitution
Solving Equations
Product and Quotient of Functions
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The circle

If you take a piece of string and secure one end, then take the other end and stretch it out and move it about 360 degrees you’ll have a circle. This means all points on the edge of the circle are an equidistant from a fixed point (the centre)
The other option is to think about the circle in terms of two stacked cones.

Take a horizontal cut, and it is the circle
The point P represents any point along the edge of the circle.

The length r, is equidistant from the centre to any point on the edge of the circle.
The equation is for a circle is r 2 = x 2 + y 2. This is the standard form of the equation, which is centered at the origin.
For circles not centered at the origin:
(x + h) 2 + (y - k) 2 = r 2, where h & k are the co-ordinates of the origin

Example 1
What is the equation of a circle (centred at the origin) with a radius of 5?
Since r = 5, we substitute that into the equation
x 2 + y 2 = (5) 2

x 2 + y 2 = 25

Example 2
Write an equation of a circle with a radius of 4, and a centre @ (3,-1). State the domain and range of the circle.
Using the equation (x + h) 2 + (y - k) 2 = r 2, the radius 4, and the centre (3,-1)
(x - 3) 2 + (y - (-1)) 2 = 4 2

(x - 3) 2 + (y +1) 2 = 16 2
Domain : { x | -1 < x < 7; x }
Range : { y | -5 < y < 3; y }

Example 3
What is the equation of the circle in standard form, with centre at (-2,3) and through the
point P(4,1)
Draw a picture to assist in the process.

Using the Pythagorean Theorem, we can find the length of the radius.

r 2 = (4 - (-2)) 2 + (1 - 3) 2

r 2 = 36 + 4

r 2 = 40
Since we know the centre, the equation is (x + 2) 2 + (y - 3) 2 = 40

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