Intersection of a Circle and a Line

Intersection of a Circle and a Line

For a circle:

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

and line:

$$Ax+By+C=0$$

let the perpendicular distance from the centre to the line be:

$$d=\frac{|Ah+Bk+C|}{\sqrt{A^2+B^2}}$$

The number of intersection points is:

$$d<r\Rightarrow\text{2 points}$$

$$d=r\Rightarrow\text{1 point}$$

$$d>r\Rightarrow\text{0 real points}$$

Usage

- Used to determine whether a line is secant, tangent or non-intersecting with a circle.