standard equation of circle

A-Maths: Find Equation of Circle Given Tangent & Circle + More

Many students after reading the question take a long time to begin as they don't know how to start. The trick is to draw! Drawing helps us to see and understand the question better.

Drawing is one of the keys to answer this question. To answer part (a), we need to notice the property of radius is perpendicular to tangent. Also, in part (b) of the question, we need to apply discriminant from the topic of Quadratic.

I have shared my thinking process and step-by-step solutions in the following videos.

How did you find the videos? Did they help you to understand better? Leave me your feedback in the comment section.

Part (a) URL: Click here to watch part (a) 7 minutes

Part (b) & (c) URL: Click here to watch part (b) & (c) 5 minutes.

A-Math: General Equation of Circle - Linked to Completing Square

In the previous post, I have discussed the standard equation of circle which is derived from distance formula.

The other equation of circle is known as General.

Example

To answer this question easily, you need your completing square technique (Read about the steps here) which many students dislike!

You notice in the step by step solution, the general equation is converted into a standard equation through the following steps:

Arrange all x terms and y terms together
Start completing square
Simplify all constants
Set equation into standard equation of circle

General Equation to Standard Equation of Circle

Radius = 5 and Centre of circe = (4, 1)

I hope you have a better understanding on equation of circle.

A-Math: Standard Equation of Circle - Derived from Distance Formula

I notice many students had a hard time making sense of the standard equation of circle which is nothing new! The standard equation of circle is simply the Distance formula learnt in Coordinate Geometry in E-Math and A-Math.

Standard equation of circle:

Example:

Test Yourself:

To ensure you have understood the standard equation of circle, attempt the question below by selecting the correct option and leave your answer in the comments section.

In my future post, I'm going to discuss the other type of equation of circle: General equation of circle.

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