School level

# 14th May

## 14th May: Coordinate Geometry of the Circle

### Learning Outcomes

In addition to the OL learning outcomes, students studying at HL should be able to:

•  Recognise that x2 + y2 + 2gx + 2fy + c = 0 represents the relationship between the x and y coordinates of points on a circle with centre (-g,-f) and radius r where  r = √ (g2 + f2 – c)
• Solve problems involving a line and a circle

Explanatory Videos
Student Activities
GeoGebra File
SEC Exam Questions

### Circle Properties - Part 1

https://youtu.be/H247_Gs6GOg Added: 20 Jun 2018 Contributor: UCD MSC Resource type: Audio / Video

Examine the terminology and properties of the circle with this informative 3-minute video clip. This video was produced by the UCD Maths Support Centre in conjunction with UCD access centre.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: Flipped learning - Assign the video as a homework task. Students watch the video at home and can then apply what they learned in the next lesson.

Asset type: Video
Language: English
Special Needs:

### Circle Properties - Part 2

https://www.youtube.com/watch?v=G_sDQb9mV3g Added: 17 Jul 2018 Contributor: UCD MSC Resource type: Audio / Video

Video investigates the properties of a circle by examining the following points:
A) Angle at the centre of circle compared with the angle at the circumstances.
B) Two angles in a circle standing on the same arc.
D) Angles in a Semicircle

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Asset type: Video
Language: English
Special Needs:

### Circle with centre at (h, k)

This student activity accompanies the GeoGebra file of the same name for students to investigate the equation of these circles.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Circle with centre at (-g, -f)

This student activity accompanies the GeoGebra file of the same name that focuses on coordinate geometry of the circle.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Equation of a circle with centre (0, 0)

https://www.geogebra.org/classic/jr2steag Added: 25 Mar 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

Use Pythagoras' theorem to discover the equation of a circle with centre (0, 0)

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Suggestions for use: This geogebra file can be used as a demonstration or an exploratory tool to show that pythagoras' theorem can be used to discover the equation of a circle.

Asset type: Online Resource
Language: English
Special Needs:

### Equation of a circle with centre (h, k)

https://www.geogebra.org/classic/ukufacyx Added: 25 Mar 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

Use Pythagoras' theorem to discover the equation of a circle when it's centre is not at (0, 0).

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Suggestions for use: This geogebra file can be used as a demonstration or an exploratory tool to show that pythagoras' theorem can be used to discover the equation of a circle.

Asset type: Online Resource
Language: English
Special Needs:

### Geogebra - Circles with centre (-g, -f)

https://www.geogebra.org/m/XK6rD007 Added: 13 May 2020 Contributor: PDST Resource type: Tool

This file accompanies the student activity sheet of the same name to allow students to investigate these circles.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Asset type: Online Resource
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### 2019 HL Paper 2 Q3

This exam question looks at the circle with coordinate geometry.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### 2019 LC HL P2 Circle Question

This exam questions looks at coordinate geometry of the line and circle

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

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