LCHL Maths – Co-ordinate Geometry of The Circle

Leaving Cert Higher Level Maths LCHL Maths – Co-ordinate Geometry of The Circle

LCHL Co-ordinate Geometry of the Circle

Your progress through this topic0 of 9 lessons

Lessons in this topic

All 9 lessons, in order — each one ticks off as you open it.

1Introduction 2Characteristics of the equation of a circle 3Proving a point is: on a circle, inside a circle or outside a circle 4Point of intersection of a line and a circle ( tangents, chords etc)5Intersecting circles/Touching circles 6Circles with the axes as a tangent 7The circle 7 Find the equation of the tangent to the circle at the point.8Find the equation of the tangent to the circle from the point.9Simultaneous Equations

Key ideas in this topic

Centre–radius form — Centre–radius formThe Circle

General form — General formThe Circle

Centre & radius from general form — Centre & radius from general formThe Circle

Methods you must know

Proving a line is a tangent — Proving a line is a tangentone solution ⇒ tangent

Circles touching externally — Circles touching externallyd = r₁ + r₂

Circles touching internally — Circles touching internallyd = |r₁ − r₂|

x-axis is a tangent — x-axis is a tangentr = |−f|, g² = c

y-axis is a tangent — y-axis is a tangentr = |−g|, f² = c

Both axes are tangents — Both axes are tangentsr = |−g| = |−f|

Check it against the exam

Jump straight to the fully worked solution for that paper.

2023 Paper 2 Q4 →2022 Paper 2 Q3 →2021 Paper 2 Q3 →2020 Paper 2 Q2 →2020 Paper 2 Q3 →

Topic Content

0% Complete 0/9 Steps

The Circle 1 – Introduction

The Circle 2 – Characteristics of the equation of a circle

The Circle 3 – Proving a point is: on a circle, inside a circle or outside a circle

The Circle 4 – Point of intersection of a line and a circle ( tangents, chords etc)

The Circle 5 – Intersecting circles/Touching circles

The circle 6: Circles with the axes as a tangent

The circle 7 Find the equation of the tangent to the circle at the point.

The circle 8 : Find the equation of the tangent to the circle from the point.

The Circle 9 – Simultaneous Equations