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.

Superprof

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 .

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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20 Apr.

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