Equation of a Circle

The standard form of the equation of a circle is $$(x - h)^2 + (y - k)^2 = r^2$$ , where (h, k) is the center and r is the radius.

To find the radius from the equation $$(x - h)^2 + (y - k)^2 = r^2$$ , take the square root of r^2.

The diameter of a circle is twice the radius, or $$d = 2r$$ .

A chord is a line segment whose endpoints lie on the circle.

A tangent is a line that touches the circle at exactly one point.

In the equation $$(x - h)^2 + (y - k)^2 = r^2$$ , the center is the point (h, k).

The area A of a circle is given by the formula $$A = \frac{1}{2} \times \text{radius}^2$$ .

If the center is (h, k) and the radius is r, the equation is $$(x - h)^2 + (y - k)^2 = r^2$$ .

This represents a circle with center (4, 3) and radius 5.

The number on the right side of the equation $$(x - h)^2 + (y - k)^2 = r^2$$ represents the square of the radius.