Comprehensive Guide to Conic Sections: Circles, Parabolas, Ellipses, and Hyperbolas

Circle

A set of points that are all the same distance from a center point.

Radius (r)

The distance from the center of the circle to any point on the circle.

Standard Equation of a Circle

$(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle.

Center of the Circle

Located at the coordinates $(h, k)$, where the signs are flipped from the equation.

Finding the Radius

Take the square root of the number on the right side of the equation to find the actual radius.

Example Equation

Given: $(x - 3)^2 + (y + 2)^2 = 4$.

Center from Example

$(3, -2)$ (using the sign flip rule).

Radius from Example

$\text{radius} = \text{sqrt}(4) = 2$.