# The Circle

**Definition of circle**

The locus of point that moves such that its distance from a fixed point called the center is constant. The constant distance is called the radius, r of the circle.

**General Equation ( C = A)**

From the general equation of conic sections,

*C*=

*A*. Hence, the equation of the circle is

$Ax^2 + Ay^2 + Dx + Ey + F = 0$

or

$x^2 + y^2 + Dx + Ey + F = 0$

**Standard Equations**

**Circle with center at any point (**

*h*,*k*)Apply Pythagorean Theorem to the figure shown below.

$(x - h)^2 + (y - k)^2 = r^2$

**Circle with center at the origin**

If the center is at the origin, (*h*, *k*) = (0, 0), hence,

$x^2 + y^2 = r^2$