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.
Calculate the points of intersection between and .