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, Discriminant, depending on the following solutions:

Circle-Line Intersection


1 Secant Line if Δ > 0

Two solutions: There are two points of intersection.

Circle-Line Intersection


2 Tangent line if Δ = 0

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

Circle-Line Intersection


3 If Δ < 0

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

Ejemplo

Calculate the points of intersection between Circle-Line Intersection Example and Circle-Line Intersection Example.




Circle-Line Intersection

Circle-Line Operations

Circle-Line Calculations

Circle-Line Calculations

Circle-Line Calculations

Circle-Line Solution