Intersection of Circles & Lines Worksheets

Printable “Systems of Equations” worksheets:
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Intersection of Circles & Lines

Examples, solutions, videos, and worksheets to help Algebra II students learn how to find the intersection of a line and a circle by solving systems of a linear and a circle equation in two variables algebraically using substitution or elimination and graphically.

How to find the Intersection of a Line and a Circle?

To find the intersection points of a circle and a line, we need to solve the system of equations formed by the equation of the circle and the equation of the line. This can yield two points, one point (if the line is tangent), or no points (if the line does not intersect the circle).

Steps to Solve

1. Write the equations:
   The general equation of a circle:(𝑥−ℎ)² + (𝑦−𝑘)² = 𝑟²
   where (h,k) is the center and 𝑟 is the radius.
   The general equation of a line:
   𝑦 = 𝑚𝑥 + 𝑐
   where 𝑚 is the slope and 𝑐 is the y-intercept.
   
2. Substitute the line equation into the circle equation.
3. Simplify and solve for 𝑥
4. Find the corresponding 𝑦-values

Have a look at this video if you need to review how to find the points of intersection between a circle and a line.

• Finding the Points of intersection between the Circle and a Line

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Intersection of Circles & Lines Worksheet #1
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Intersection of Circles & Lines

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