12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and...

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12-5 Circles in the Coordinate Plane

Transcript of 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and...

Page 1: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

12-5 Circles in the Coordinate Plane

Page 2: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Theorem 12-13

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

(x - h)2 + (y - k)2 = r2

“standard form”

Page 3: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #1

• Write the equation (in standard form) of the circle with center at (4,-1) and radius 3.

(x - h)2 + (y - k)2 = r2

Page 4: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #1

• Write the equation (in standard form) of the circle with center at (4,-1) and radius 3.

(x - 4)2 + (y - k)2 = r2

Page 5: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #1

• Write the equation (in standard form) of the circle with center at (4,-1) and radius 3.

(x - 4)2 + (y – (-1))2 = r2

Page 6: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #1

• Write the equation (in standard form) of the circle with center at (4,-1) and radius 3.

(x - 4)2 + (y – (-1))2 = 32

Page 7: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #1

• Write the equation (in standard form) of the circle with center at (4,-1) and radius 3.

(x - 4)2 + (y +1)2 = 32

Page 8: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #1

• Write the equation (in standard form) of the circle with center at (4,-1) and radius 3.

(x - 4)2 + (y +1)2 = 9

Page 9: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #2

• Write the equation (in standard form) of the circle with center at (4,-1) and passes through the point (1, 3).

212

212 )()( yyxxd

Page 10: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #2

• Write the equation (in standard form) of the circle with center at (4,-1) and passes through the point (1, 3).

22 ))1(3()41( d

Page 11: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #2

• Write the equation (in standard form) of the circle with center at (4,-1) and passes through the point (1, 3).

22 )4()3( d

Page 12: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #2

• Write the equation (in standard form) of the circle with center at (4,-1) and passes through the point (1, 3).

169d

Page 13: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #2

• Write the equation (in standard form) of the circle with center at (4,-1) and passes through the point (1, 3).

25d

Page 14: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #2

• Write the equation (in standard form) of the circle with center at (4,-1) and passes through the point (1, 3).

5d

Page 15: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Example #2

• Write the equation (in standard form) of the circle with center at (4,-1) and passes through the point (1, 3).

5d(x-4)2 + (y+1)2 = 25

Page 16: 12-5 Circles in the Coordinate Plane. Theorem 12-13 An equation of a circle with center (h,k) and radius r is (x - h) 2 + (y - k) 2 = r 2 standard form.

Today’s Assignment

• P. 697 #1-21 (do not graph!)


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