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Circle Equations: Understanding, Graphing, and Solving

Explore the equation of a circle, its center, radius, and how to find intersection points with other equations. Learn how to graph circles and identify key properties. Master conic sections with clear examples.

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Circle Equations: Understanding, Graphing, and Solving

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  1. Circles

  2. The equation of a circle • What characterizes every point (x, y) on the circumference of a circle?

  3. Every point (x, y) is the same distance r from the center.  Therefore, according to the Pythagorean distance formulafor the distance of a point from the origin:

  4. The equation of a circle of radius r, with center at the origin (0, 0). • Where r is the radius. • The center of the circle, (0,0) is its Locator Point.

  5. Examples • x² + y² = 64 • (x-3)² + y² = 49 • x² + (y+4)² = 25 • (x+2)² + (y-6)² = 16

  6. Circles Translated and Stretched (x-h)² + (y-k)² = r²

  7. (x-h)² + (y-k)² = r² • x² + (y-3)² = 4²

  8. (x-h)² + (y-k)² = r² • (x-1)² + (y-1)² = 25

  9. CirclesExample 1 Write the equation of the circle with the point (4,5) on the circle and the origin as it’s center.

  10. Example 1 Point (4,5) on the circle and the origin as it’s center.

  11. Example 2Find the intersection points on the graph of the following two equations

  12. Now what??!!??!!??

  13. Example 2Find the intersection points on the graph of the following two equations Plug these in for x.

  14. Example 2Find the intersection points on the graph of the following two equations Back to Conics

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