Last updated on Sep 20, 2026

Advanced Applications of Transformations (HSC SSCE Mathematics Advanced): Flashcards

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Circles and Translations

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Standard form of circle centred at origin

$x^2 + y^2 = r^2$

Centre of circle $(x - a)^2 + (y - b)^2 = r^2$

$(a, b)$

Radius from $(x - a)^2 + (y - b)^2 = r^2$

$r$ (positive only)

Domain of circle with centre $(a, b)$ and radius $r$

$[a - r, a + r]$

Range of circle with centre $(a, b)$ and radius $r$

$[b - r, b + r]$

General form of circle equation

$x^2 + y^2 + ax + by + c = 0$

Method to convert general form to standard form

Complete the square for $x$ and $y$ terms

Why radius must be positive

Radius is a distance (always positive scalar)

Translation when $a > 0$ in $(x - a)^2 + (y - b)^2 = r^2$

Circle moves right

Translation when $b > 0$ in $(x - a)^2 + (y - b)^2 = r^2$

Circle moves up

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Advanced Applications of Transformations (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

Standard form of circle centred at origin

Centre of circle (x−a)2+(y−b)2=r2(x - a)^2 + (y - b)^2 = r^2(x−a)2+(y−b)2=r2

Radius from (x−a)2+(y−b)2=r2(x - a)^2 + (y - b)^2 = r^2(x−a)2+(y−b)2=r2

Domain of circle with centre (a,b)(a, b)(a,b) and radius rrr

Range of circle with centre (a,b)(a, b)(a,b) and radius rrr

General form of circle equation

Method to convert general form to standard form

Why radius must be positive

Translation when a>0a > 0a>0 in (x−a)2+(y−b)2=r2(x - a)^2 + (y - b)^2 = r^2(x−a)2+(y−b)2=r2

Translation when b>0b > 0b>0 in (x−a)2+(y−b)2=r2(x - a)^2 + (y - b)^2 = r^2(x−a)2+(y−b)2=r2

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Centre of circle $(x - a)^2 + (y - b)^2 = r^2$

Radius from $(x - a)^2 + (y - b)^2 = r^2$

Domain of circle with centre $(a, b)$ and radius $r$

Range of circle with centre $(a, b)$ and radius $r$

Translation when $a > 0$ in $(x - a)^2 + (y - b)^2 = r^2$

Translation when $b > 0$ in $(x - a)^2 + (y - b)^2 = r^2$