Conic Sections/Circle

Definition

The circle is the simplest and best known conic section. The geometric definition of a circle is the locus of all points a set distance r from a point called the center. The general equation for a circle with center (h,k) and radius r is $(x-h{)}^2+(y-k{)}^2=r^2$. For a circle, the radius (r) must be greater than 0, however if r=0, the graph is a single point.

Standard form

The standard form of a circle equation is Ax²+By²+Cx+Dy+E=0

Example

Find the center and the radius of the following circle: x²+y²+8x-10y+20=0

x²+y²+8x-10y+20=0
-20-20
x²+y²+8x-10y= - 20
(x²+8x)+(y²-10y)= - 20
+16 +25 +16+25
(x²+8x+16)+(y²-10y+25)=21
(x+4)²+(y-5)²=21

Thus:
C(-4,5) radius=$radical(21)$