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Circles in the Coordinate Plane

Circles in the Coordinate Plane. Objectives: 1) To write an equation of a circle. 2) To find the center & radius of a circle. Equation for a Circle. Thm(11 – 13) An equation of a circle with center (h, k) & radius (r):. x-coordinate of center. y-coordinate of center.

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Circles in the Coordinate Plane

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  1. Circles in the Coordinate Plane Objectives: 1) To write an equation of a circle. 2) To find the center & radius of a circle.

  2. Equation for a Circle • Thm(11 – 13) An equation of a circle with center (h, k) & radius (r): x-coordinate of center y-coordinate of center (x – h)2 + (y – k)2 = r2 (x, y) r (h, k)

  3. Ex.1: Write the Equation of a circle. • Write the standard equation of a circle with center (-8, 1) and radius of √5. • Graph it. (x – h)2 + (y – k)2 = r2 (x – (-8))2 + (y – 1)2 = (√5)2 (x + 8)2 + (y – 1)2 = 5 √5 1 -8

  4. Ex.2: Find the center and radius of a circle with the following equation. • Equation: (x – 4)2 + (y + 2)2 = 25 • Center (4, -2) • Radius = 5

  5. Ex.3: Graph the circle with the following Equation • (x + 4)2 + (y – 1)2 = 36 • Center: (-4, 1) • Radius: 6 (x – (-4))2 + (y – 1)2 = (√36)2 1 2 -4

  6. Ex.4: Write the equation of a circle from its graph. (x – h)2 + (y – k)2 = r2 (x – 0)2 + (y – 0)2 = 42 x2 + y2 = 16 4

  7. Ex.4: More Circles Write the standard equation of a circle with center (5, 8) & passes through point (-15, -13). Step 1: Solve for r Step 2: Put into standard equation h k x y (x – h)2 + (y – k)2 = r2 (-15 – 5)2 + (-13 - 8)2 = r2 -202 + -212 = r2 400 + 441 = r2 841 = r2 29 = r (x – h)2 + (y – k)2 = r2 (x – 5)2 + (y – 8)2 = 292 (x – 5)2 + (y – 8)2 = 841

  8. What have we learned?? (x – h)2 + (y – k)2 = r2 x-coordinate of a point on a circle y-coordinate of a point on a circle Radius x-coordinate of the center of the circle y-coordinate of the center of the circle

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