# Circle-Line Intersection

To find the common points of a circle and a line, solve the systems formed by the equations of both.

In general, a quadratic equation is obtained, which will have a sign for the discriminant, , depending on the following solutions:

1 Secant Line if** Δ > 0**

Two solutions: There are two points of intersection.

2 Tangent line if** Δ = 0**

One solution: the line is a tangent to the circle.

3 If **Δ < 0 **

No solution: There is no intersection between the line and circle.

## Ejemplo

Calculate the points of intersection between and .

Subject

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