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Equations of Circles and Intersection with Lines

This guide covers how to write the equations of circles given their centers and radii, as well as strategies for finding intersections between circles and lines. Start with the general form of a circle's equation and apply it to specific points. Learn through practical examples, such as finding circles on a coordinate grid and determining intersection points with lines. Additionally, explore how to find intersections of two circles, including cases where there may be no solutions.

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Equations of Circles and Intersection with Lines

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  1. Write the equation of a circle with a center of (-7, 3) and a radius of 8. 2. Write the equation of a circle with a center of (-1, -1) that goes through the point (2, -1). 3. Write the equation of the circle pictured. Starter Activity

  2. Solving Systems involving Circles

  3. circle and a lineCircle and a circle

  4. Step 1: Graph the circle and the line on the SAME coordinate grid. • Step 2: Find the point(s) of intersection. • Step 3: Check the intersection(s) with your calculator. Circle and a Line

  5. Find the point(s) of intersection of: Solutions: (1, -1) & (3, -3) Example 1

  6. Find the point(s) of intersection of: and Solutions: (2, 2) & (-4, 2) Example 2

  7. Step 1: Graph the circle and the line on the SAME coordinate grid. • Step 2: Find the point(s) of intersection. • Step 3: Check the intersection(s) with your calculator. Circle and a Circle

  8. Find the intersection of: and Solution: NO Intersection Example 1

  9. Find the intersection of: and Solution: (2, 1) Example 2

  10. Find the intersection of: and Solutions: (3, 2) & (0, -1) Example 3

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