Equation of a Circle Centered at a Point: Explained and Solved Examples

The video tutorial explains the equations of circles centered at a specific point (a,b) and at the origin (0,0). It covers the general formula for these equations, relates them to Pythagoras' theorem, and provides examples of calculating the equation of a circle given its center and a point on its circumference. The tutorial also discusses translating circles from the origin to another point and expanding the equations into different forms.

What is the general formula for the equation of a circle centered at the origin?

How can the equation of a circle centered at a specific point a,b be expressed?

Explain how to calculate the radius of a circle given its center and a point on the circumference.

What does the expression x minus a represent in the context of a circle?

How would you write the equation of a circle with a center at -3, 4 and a radius of 3?

Describe the process of translating a circle from the origin to a new center point.

What are the steps to convert the equation of a circle into the form x squared plus y squared plus Ax plus By plus C equaling 0?