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11.5 Circles in the Coordinate Plane

11.5 Circles in the Coordinate Plane. Chapter 11 Circles Bellwork: pg 615 1-3. You can use the Distance Formula to find an equation of a circle with center ( h, k ) and radius r . Let ( x, y ) be any point on the circle. Then the radius r is the distance from ( h, k ) to ( x, y ).

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11.5 Circles in the Coordinate Plane

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  1. 11.5 Circles in the Coordinate Plane Chapter 11 Circles Bellwork: pg 615 1-3

  2. You can use the Distance Formula to find an equation of a circle with center (h, k) and radius r. Let (x, y) be any point on the circle. Then the radius r is the distance from (h, k) to (x, y). r = √(x – h)2 + (y – k)2 Distance Formula r2 = (x – h)2 + (y – k)2 Square Both Sides Theorem 11-13 An equation of a circle with center (h, k) and radius r is r2 = (x – h)2 + (y – k)2

  3. Standard Equation of a Circle (x – h)2 + (y – k)2 = r2 Write the standard equation of the circle with center (5, -2) and radius 7. (x – h)2 + (y – k)2 =r2 (x – 5)2 + (y – (-2))2 =72 (x – 5)2 + (y + 2)2 =49

  4. Write the standard equation of each circle. Standard Equation of a Circle (x – h)2 + (y – k)2 = r2 center (3, 5); radius 6 center (-2, -1); radius √2 (x – h)2 + (y – k)2 =r2 (x – h)2 + (y – k)2 =r2 (x – 3)2 + (y – 5)2 =62 (x – (-2))2 + (y – (-1))2 =(√2)2 (x + 2)2 + (y + 1)2 =2 (x – 3)2 + (y - 5)2 =36

  5. Write the standard equation of the circle with center (1, -3) that passes through the point (2, 2). Standard Equation of a Circle (x – h)2 + (y – k)2 = r2 (x – h)2 + (y – k)2 =r2 (x – h)2 + (y – k)2 =r2 (x – 1)2 + (y – (-3))2 =26 (2 – 1)2 + (2 – (-3))2 =r2 (x – 1)2 + (y + 3)2 =26 (1)2 + (5)2 =r2 1 + 25=r2 26=r2

  6. Write the standard equation of the circle with center (2, 3) that passes through the point (-1, 1). Standard Equation of a Circle (x – h)2 + (y – k)2 = r2 (x – h)2 + (y – k)2 =r2 (x – h)2 + (y – k)2 =r2 (x – 2)2 + (y – 3)2 =13 ((-1) – 2)2 + (1 – 3)2 =r2 (x – 2)2 + (y - 3)2 =13 (-3)2 + (-2)2 =r2 9 + 4=r2 13=r2

  7. Standard Equation of a Circle (x – h)2 + (y – k)2 = r2 Find the center and radius of the circle with equation (x – 7)2 + (y + 2)2 =64 (x – 7)2 + (y +2)2 =64 Center: (7, -2) Radius: 8 To graph the circle: Place the compass point at (7, -2) and draw a circle with a radius of 8.

  8. Standard Equation of a Circle (x – h)2 + (y – k)2 = r2 Find the center and radius of the circle with equation (x – 2)2 + (y – 3)2 =100 (x – 2)2 + (y - 3)2 =100 Center: (2, 3) Radius: 10 To graph the circle: Place the compass point at (2, 3) and draw a circle with a radius of 10.

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