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10-2: Conic Sections - Circles

10-2: Conic Sections - Circles. circle. Circle. The set of all co-planar points equidistant from a fixed point (center). radius. Circle. Equation: (x – h ) 2 + (y – k ) 2 = r 2. (x – h ) 2 + (y – k ) 2 = r. (x, y). r. (h, k). Circle. (x – 3) 2 + (y – 5) 2 = 121.

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10-2: Conic Sections - Circles

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  1. 10-2: Conic Sections - Circles circle

  2. Circle The set of all co-planar points equidistant from a fixed point (center). radius

  3. Circle Equation: (x – h)2 + (y – k)2 = r2 (x – h)2 + (y – k)2 = r (x, y) r (h, k)

  4. Circle (x – 3)2 + (y – 5)2 = 121 x – 3 = 0 r = 121 x = 3 r = 11 11 y – 5 = 0 (3, 5) y = 5 center (3, 5)

  5. Circle (x + 5)2 + (y – 2)2 = 81 x + 5 = 0 r = 81 x = -5 r = 9 9 y – 2 = 0 (-5, 2) y = 2 center (-5, 2)

  6. Graph the following circle 9x2 + 36x + 9y2 - 18y - 10 = 89 9x2 + 36x + 9y2 - 18y = 89 + 10 Remember when completing the square, the coefficient of the squared term must be 1 9x2 + 36x + 9y2 - 18y = 99 9 (x2 + 4x + 22 ) + (y2 - 2y + (-1)2 ) = 11 + 4 + 1 (x + 2)2 + (y - 1)2 = 16

  7. Circle (x + 2)2 + (y – 1)2 = 16 x + 2 = 0 r = 16 x = -2 r = 4 4 y – 1 = 0 (-2, 1) y = 1 center (-2, 1)

  8. Graph the following circle 4x2 + 24x + 4y2 + 32y + 13 = 157 4x2 + 24x + 4y2 + 32y = 157 - 13 4x2 + 24x + 4y2 + 32y = 144 4 (x2 + 6x + 32 ) + (y2 + 8y + 42 ) = 36 + 9 + 16 (x + 3)2 + (y + 4)2 = 61

  9. Circle (x + 3)2 + (y + 4)2 = 61 x + 3 = 0 r = 61 x = -3 61 y + 4 = 0 (-3, -4) y = -4 center (-3, -4)

  10. Graph the following circle 5x2 - 80x + 5y2 + 20y - 34 = 106 5x2 - 80x + 5y2 + 20y = 106 + 34 5x2 - 80x + 5y2 + 20y = 140 5 (x2 - 16x + (-8)2 ) + (y2 + 4y + 22 ) = 28 + 64 + 4 (x - 8)2 + (y + 2)2 = 96

  11. Circle (x - 8)2 + (y + 2)2 = 96 x - 8 = 0 r = 96 x = 8 r = 4 6 4 6 y + 2 = 0 (8, -2) y = -2 center (8, -2)

  12. Graph the following circle 2x2 + 10x + 2y2 + 8y + 4 = 25 2x2 + 10x + 2y2 + 8y = 25 - 4 2x2 + 10x + 2y2 + 8y = 21 2 (x2 + 5x + ) + (y2 + 4y + 22 ) = + + 4 (x + )2 + (y + 2)2 =

  13. Circle (x + )2 + (y + 2)2 = x + = 0 r = x = r = y + 2 = 0 y = -2 center

  14. Find the equation of the circle such that the endpoints of a diameter are (2,7) and (-6, 15). Center: use midpoint formula radius: use distance formula (h,k) = radius

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