circles date: _____________. circles standard equation of a circle 9.3 circles (x – h) 2 + (y –...

Circles Date: _____________

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Circles

Date: _____________

Circles

Standard Equation of a Circle

9.3 Circles

(x – h)2 + (y – k)2 = r2

center: (h, k)

radius: r

Write the equation of the circle that whose center is at (-2,4) and whose

radius is 3.

2 2 2( ) ( )x h y k r 2 2 2( 2) ( 4) 3x y 2 2( 2) ( 4) 9x y

Page 4: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Write the equation of the circle that whose center is at (-1,-6) and

whose radius is 6.

2 2 2( ) ( )x h y k r 2 2 2( 1) ( 6) 6x y 2 2( 1) ( 6) 36x y

Page 5: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Write the equation of the circle that whose center is at (0,4) and whose

radius is 2.

2 2 2( ) ( )x h y k r 2 2 2( 0) ( 4) 2x y

2 2( 4) 4x y

Page 6: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Find the center and radius of the circle. Then write the equation of

the circle.

yCenter =

Radius =

(1,2)

2 2 2( 1) ( 2) 3x y 2 2( 1) ( 2) 9x y

Page 7: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Find the center and radius of the circle. Then write the equation of

the circle.

yCenter =

Radius =

(-1,0)

2 2 2( 1) ( 0) 4x y 2 2( 1) 16x y

Page 8: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Find the center and radius of the circle. Then graph the circle.

2 2( 1) ( 3) 16x y

Center =

Radius =

(-1,3)

Find the center and radius of the circle. Then graph the circle.

2 2( 3) ( 2) 4x y

Center =

Radius =

(-3,-2)

Find the center and radius of the circle. Then graph the circle.

2 2( 4) ( 1) 25x y

Center =

Radius =

(4,1)

Complete the square.

x2 + 10x

1. 10 2 = 52. 52 = 253. x2 + 10x + 254. (x + 5)(x + 5)5. (x + 5)2

Page 12: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Complete the square.

x2 – 20x

1. -20 2 = -102. (-10)2 = 1003. x2 – 20x + 1004. (x – 10)(x – 10)5. (x – 10)2

Page 13: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Completing the Square to Write Standard Equations of Circles

1. Add/subtract to move the constant term to the other side of the equation.

2. Rearrange the terms so that the x’s and y’s are together.

3. Complete the square for the x’s and y’s.

4. Make sure that anything you added to the one side of the equation is added to the other side as well.

Page 14: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Write the equation of the circle in standard form. Then find the center

and radius of the circle.

x2 + y2 + 4x – 6y – 3 = 0

x2 + 4x + y2 – 6y = 3

x2 + y2 + 4x – 6y = 3

x2 + 4x + ___ + y2 – 6y + ___ = 34 + 49 + 9

x2 + 4x + 4 + y2 – 6y + 9 = 16

(x + 2)2 + (y – 3)2 = 16 Center = (-2, 3)

Radius = 4

Page 15: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Write the equation of the circle in standard form. Then find the center

and radius of the circle.

x2 + y2 – 12x – 2y – 8 = 0

x2 – 12x + y2 – 2y = 8

x2 + y2 – 12x – 2y = 8

x2 – 12x + ___ + y2 – 2y + ___ = 836 +361 +1

x2 – 12x + 36 + y2 – 2y + 1 = 45

(x – 6)2 + (y – 1)2 = 45 Center = (6, 1)Radius = √45 ≈ 6.7

Page 16: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Write the equation of the circle in standard form. Then find the center

and radius of the circle.

x2 + y2 – 10x + 4y + 17 = 0

x2 – 10x + y2 + 4y = -17

x2 + y2 – 10x + 4y = -17

x2 – 10x + ___ + y2 + 4y + ___ = -1725 +254 +4

x2 – 10x + 25 + y2 + 4y + 4 = 12

(x – 5)2 + (y + 2)2 = 12 Center = (5, -2)Radius = √12 ≈ 3.5

Page 17: Circles Date: _____________. Circles Standard Equation of a Circle 9.3 Circles (x – h) 2 + (y – k) 2 = r 2 center: (h, k) radius: r

Write the equation of the circle that passes through the given point and has a center at the

origin.

(-5, -12)

2 2

2 1 2 1d x x y y

2 25 0 12 0d

2 25 12d

25 144d

169d

13d 2 2 169x y

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