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.
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One of the first topics that many Secondary 4 E-Math students learnt is a statistics chapter known as Mean and Standard Deviation (SD for short).
The nice thing about this chapter is that the 2 most important formula are both available in the E-Math (subject code: 4016) formula sheet! No memorization required, just understanding of their usage.
In this post, I will illustrate 2 methods to get the answers for mean and SD for ungrouped data (refer to example). The 2 methods are manual and calculator.
Example:
Given 15, 6, 18, 9, 2 and 4, find the mean and standard deviation.
Manual:
Mean and Standard Deviation Manual Working
Calculator, Casio fx-85MS:
- Mode, 2(SD)
- Enter the data in this manner, 15, M+ follows by 6, M+…
- To get mean: Press ‘Shift’, 2, 1,=
- To get SD: Press ‘Shift’, 2, 2,=
Here are some additional information you can obtain using the calculator:
Mean - SD from Calculator
Answers obtained through both methods are the same. By knowing these 2 methods, you can use either to double check.
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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.
Diagram for Standard Eqn of Circle
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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Hi,
I'm Ai Ling. I enjoy coaching students who have challenges with
understanding and scoring in 'O' Level A-Maths and E-Maths. 
