Circle


 1

Introduction

A brief introduction to the topic Circle in coordinate geometry

2

Definition and Standard Equation

Definition of a circle. Derivation of the standard equation of a circle.

3

Equation: Part 1

Equation of a circle with known center and radius. General equation of a circle.

4

Equation: Examples

A few examples focused on equations of a circle in the Cartesian plane

5

Equations: More Examples

A few examples focused on equations of a circle in the Cartesian plane

6

Equation: Part 2

Equation of a circle with known end points of diameter. Another definition of a circle.

7

Equation: Even More Examples

A few examples focused on equations of a circle in the Cartesian plane

8

Parametric Equation

Derivation of the parametric equation of the circle

9

Position of a Point

Conditions for a point to be inside, on, or outside a given circle

10

Position of a Point: Examples

A few examples to illustrate the concept of position of a point relative to a circle.

11

Intersection with a Line: Part 1

Position of a line with respect to a circle.

12

Intersection with a Line: Examples

A few examples to illustrate the position of a line with respect to a circle.

13

Intersection with a Line: Part 2

Length of a Chord intercepted by a line

14

Intersection with a Line: Examples

A few examples to illustrating the calculation of length of a chord of a circle

15

Tangent – Slope Form: Part 1

Condition for a line to become a tangent to a circle

16

Tangent – Slope Form: Part 2

Equation of the tangent to a circle in slope form, and coordinates of the point of contact

17

Tangent – Slope Form: Examples

Solved examples to illustrate slope form of tangents to a circle.

18

Tangent – Point Form

Equation of a tangent to a circle at a given point, or equation of a tangent in ‘point form’

19

Tangent – Point Form: Examples

A few solved examples relating to equation of a tangent to a circle

20

Tangent from an External Point: Part 1

Equation of the tangent to a circle from an external point.

21

Tangent from an External Point: Part 2

Angle between tangents to a circle from an external point.

22

Tangent from an External Point: Part 3

Length of a tangent to a circle from an external point.

23

Tangent from an External Point: Examples

A few solved examples relating to tangents to a circle from an external point

24

Normal

Definition of Normal to a Circle.

25

Normal: Equations

Equations of normal in various forms, to a circle.

26

Normal: Examples

A few examples related to equations of normal to a circle.

27

Normal – Shortest Distance: Part 1

Shortest distance between a line and a point, and between a point and a circle.

28

Normal – Shortest Distance: Part 2

Shortest distance between a line and a circle, and between two circles.

29

Normal – Shortest Distance: Examples

A few examples illustrating the shortest distance between a circle and a point, a line or another circle.

30

Two Circles – Relative Position

Relative position of two circles, based on their radii and coordinates of centres.

31

Two Circles – Relative Position: Examples

A few examples illustrating relative position of two circles in the Cartesian plane.

32

Two Circles – Number of Common Tangents

Number of common tangents to two circles, based on their relative position

33

Two Circles – Equations of Common Tangents

Equations of common tangents to two circles

34

Two Circles – Equations of Common Tangents: Examples

Examples illustrating finding the equations of common tangents to two circles

Cheat Sheet

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