Equations of Circles

Equations of Circles is AMO (Acc. math objective) number 60. We start the lesson off by Mr. Maksymchuk reminding us that a circle is a relation because of it failing the vertical line test. Two things about a circle that you can change are:

1. LOCATION / POSITION (coordinates of center)

2. SIZE (based on radius of diameter)

The next thing we did was play around with Graphmatica and learned that if you put x^2+y^2=e^2 (x squared + y squared = radius squared) it makes a circle. Then we learned that if you put the x and y in ( ) then you can add values to them, such as (x-8)^2+(y-7)^2=4. This made a circle in the positive quadrant which was interesting because of the equation haves -8 and -7. However when you put +8 and +7 it goes into the negative quadrant.

This is why the circles go where they go in the quadrants.

Mr. Maksymchuk then showed us how to do two of Mikayla's problems, as shown below: