In this resource, you will master the graphing of a circle when given an equation of a circle – in any form. You will understand the changes in the values of the coefficient and constants in the equation and how those changes are represented on the graph.

Conics are figures or shapes that are realized by slicing a cone at different angles. The following link will take you to a website where you can see a good representation of the slicing of a cone, read a short mathematical history of conics, and view several examples of conics in the real world and their uses: Occurrence of the Conics

Definition of a Circle—The set of all points in a plane equidistant from a given point, known as the center.

The standard form of any conic section is Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are real numbers.

In a circle, it is always true that A = C and both A and C are positive

The “graph” form of the equation of a circle is: a(x - h)² + b(y - k)² = r²

• a and b are real numbers and a = b,
• the point (h, k) is the center of the circle,
• and r is the radius of the circle.