The equation of a circle with center (h, k) and radius r ... · general del circulo con centro (h, k) y radio r. The equation of a circle with center (h, k) and radius r is Examples

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Math 2 Lesson 10.5: The Equation of a Circle

A circle is the set of points in a plane that are a fixed distance, called the radius from a fixed point, called the center

Un círculo es un set de puntos en un plano a una distancia fija llamada el radio de un punto fijo, llamado el centro.

Notice that r2 and the center are visible in the equation of a circle. This leads to a general formula for a circle with center (h, k) and radius r.

Nota que r2 y el centro son visibles en la ecuación del círculo. Esto te lleva a la formula general del circulo con centro (h, k) y radio r.

The equation of a circle with center (h, k) and radius r is

Examples

Write the equation of a circle with center (–3, 4) and radius r = 6. Escribe la ecuación de un circulo con centro (–3, 4) y radio r = 6. Find the equation of the circle with center (5, -2) and radius r = 8. Encuentra la ecuación del circulo con centro (5, -2) y radio r = 8.

Graph x2 + y2 = 16 Graph (x – 3)2 + (y + 4)2 = 9 Graph (x + 1)2 + (y – 3)2 = 25

Use the information provided to write the standard form equation of each circle.

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CLASSWORK Write the equation of each circle.

Circle with center (4, 2) and radius r = 7.

Circle with center (1, –5) and a radius of 10.

Circle with center (2, 1) and radius r = 5.

Graph the following circles: x² + y² = 9 (x – 3)2 + (y + 2)2 = 4 x² + y² = 4 (x – 2)2 + (y + 4)2 = 16

Use the information provided to write the standard form equation of each circle.

�J with center (2, 2) and radius 4 �P with center (0, –3) and radius 8 �L with center (–5, –6) and radius 9

CLASSWORK KEY Write the equation of each circle.

Circle with center (4, 2) and radius r = 7.

Circle with center (1, –5) and a radius of 10.

Circle with center (2, 1) and radius r = 5.

Graph the following circles:

Use the information provided to write the standard form equation of each circle.

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�J with center (2, 2) and radius 4 �P with center (0, –3) and radius 8 �L with center (–5, –6) and radius 9