The Equation of a Circle

A short animation showing how the equation of a circle, (x-h)^2+(y-k)^2=r^2, comes from the Pythagorean theorem applied to a point on the circle, its center, and the radius. The center and radius are plotted first, then a moving point traces the circle while right triangles form to show why the distance formula leads to this equation. Useful for students learning coordinate geometry and conic sections.

Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy

The prompt that made it

Create circle equation ani ation 30 second bes practise animation video

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Make the next one in this series

• Animate how changing h, k, and r shifts and resizes the circle on the coordinate plane
• Show how to convert a general quadratic equation into standard circle form by completing the square
• Illustrate the relationship between a circle's equation and its tangent line at a given point

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