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circle

circle. Jeff Bivin -- LZHS. Circle. The set of all points equidistant from a fixed point (center). radius. Jeff Bivin -- LZHS. Circle. Equation: x 2 + y 2 = r 2 ( x – h ) 2 + (y – k ) 2 = r 2. r. (h, k). Jeff Bivin -- LZHS.

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circle

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  1. circle Jeff Bivin -- LZHS

  2. Circle The set of all points equidistant from a fixed point (center). radius Jeff Bivin -- LZHS

  3. Circle Equation: x 2 + y2 = r2 (x – h)2 + (y – k)2 = r2 r (h, k) Jeff Bivin -- LZHS

  4. Derive equation of circle • https://www.khanacademy.org/math/geometry/cc-geometry-circles/equation-of-a-circle/v/equation-for-a-circle-using-the-pythagorean-theorem

  5. Circle x 2+ y 2= 16 center r = (0, 0) 16 r = 4 4 (0, 0) Jeff Bivin -- LZHS

  6. 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) Jeff Bivin -- LZHS

  7. Circle (x + 5)2 + (y – 2)2 = 81 center r = 81 r = 9 ( -5 , 2 ) 9 (-5, 2) Jeff Bivin -- LZHS

  8. Graph the following circle: x2+ 4x + y2- 2y - 10 = 1 x2+ 4x + y2- 2y = 1+ 10 x2+ 4x + y2- 2y = 11 (x2 + 4x + 22 ) + (y2 - 2y + (-1)2 ) = 11 + 4 + 1 (x + 2)2 + (y - 1)2 = 16 Jeff Bivin -- LZHS

  9. Circle (x + 2)2 + (y – 1)2 = 16 r = center 16 r = 4 4 (-2, 1) (-2, 1) Jeff Bivin -- LZHS

  10. Circle r = center 16 r = 4 (-2, 1) 4 (x + 2)2 + (y – 1)2 = 16 (-2, 1) Intercepts: x-int: (Plug 0 in for y) y-int: (Plug 0 in for x) (x + 2)2 + (y – 1)2 = 16 (x + 2)2 + (y – 1)2 = 16 (0 + 2)2 + (y – 1)2 = 16 (x + 2)2 + (0 – 1)2 = 16 4 + (y – 1)2 = 16 (x + 2)2 + 1 = 16 (y – 1)2 = 12 (x + 2)2 = 15 y – 1 = ±√12 x + 2 = ±√15 y = 1 ±2√3 x = -2 ± √15 y = 4.46 or -2.46 x = -5.87 or 1.87

  11. 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 + 4y + 22 ) = 36 + 9 + 4 (x + 3)2 + (y + 2)2 = 49 Jeff Bivin -- LZHS

  12. Circle r = (x + 3)2 + (y + 2)2 = 49 center 49 r = 7 (-3, -2) x-int: (Plug 0 in for y) y-int: (Plug 0 in for x) 7 (x + 3)2 + (y + 2)2 = 49 (0 + 3)2 + (y + 2)2 = 49 (x + 3)2 + (0 + 2)2 = 49 9 + (y + 2)2 = 49 (x + 3)2 + 4 = 49 (y + 2)2 = 40 (x + 3)2 = 45 (-3, -2) y + 2 = 40 ±√ x + 3 = ±√ 45 y = -2 ±2√10 x = -3 ±3√5 x = 3.71 or -9.71 y = 4.32 or -8.32 Jeff Bivin -- LZHS

  13. Graph the following circle: 5x2 - 80x + 5y2 + 20y - 34 = 106 5x2 - 80x + 5y2 + 20y = 106 + 34 5x2 - 80x + 5y2 + 20y = 140 5 (x2 - 16x + 42 ) + (y2 + 4y + 22 ) = 28 + 16 + 4 (x - 4)2 + (y + 2)2 = 48 Jeff Bivin -- LZHS

  14. Circle (x - 4)2 + (y + 2)2 = 48 center r = 48 r = 4 3 4 3 (4, -2) (4, -2) Jeff Bivin -- LZHS

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