Circles and Coordinate Geometry
Aligned to G-GPE.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
The equation of a circle comes from the distance formula: every point on the circle is the same distance, the radius, from the center. A circle centered at (h, k) with radius r has the equation (x - h) squared plus (y - k) squared equals r squared.
Worked example
A circle centered at (0, 0) with radius 5 has the equation x squared plus y squared equals 25, since 5 squared is 25.
Practice questions
- Write the equation of a circle at the origin with radius 3.
- What is the radius if the equation is x squared + y squared = 49?
- What is the center of (x - 2) squared + (y + 1) squared = 16?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Círculos y geometría en el plano coordenado
La ecuación de un círculo proviene de la fórmula de la distancia: cada punto del círculo está a la misma distancia —el radio— del centro. Un círculo con centro en (h, k) y radio r tiene la ecuación (x - h) al cuadrado más (y - k) al cuadrado igual a r al cuadrado.
Ejemplo: Un círculo con centro en (0, 0) y radio 5 tiene la ecuación x al cuadrado más y al cuadrado igual a 25, ya que 5 al cuadrado es 25.
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