Name:__________________________________________Date:________________Period:______________ 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 r 2 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 r 2 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 x 2 + y 2 = 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. A) B) I O y 59 CG , 3) opposite , 8=3 ( xt35ttf-H-%eaG-Btly.IE#rr--IC--kQI - ItF3)⇒ i . . . . o ;±←*'÷ e . Y÷÷¥¥¥
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Name:__________________________________________Date:________________Period:______________
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.
A) B)
I
Oy 59 CG ,3)opposite , 8=3
(xt35ttf-H-%eaG-Btly.IE#rr--IC--kQI- ItF3)⇒
i. .
.
.
o ;±←*'÷ e. Y÷÷¥¥¥
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.
+ ) െ ) = ( െ ) + +) ) =
) െ ) + = ) ૢ െ ) + +) ) =
�J with center (2, 2) and radius 4 �P with center (0, –3) and radius 8 �L with center (–5, –6) and radius 9
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