Directions: Write The Equation (In Center-Radius Form) Of Each Of The Following Circles Given The Ce

Directions: Write the equation (in center-radius form) of each of the following circles given the center and the radius. Write your answers on a separate sheet of paper. Equation Center Radius (Center-Radius Form) 1. origin 2 2. (1, 2) 5 3. ( 36) 11 4. (-2,-7) 15 5, (-5,8) 3/

 

✒️CIRCLE EQUATION

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\largenderline{\mathbb{DIRECTIONS}:}

  • Write the equation (in center-radius form) of each of the following circles given the center and the radius. Write your answers on a separate sheet of paper.

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\largenderline{\mathbb{ANSWERS}:}

\quad \large \rm{1) \; x^2 + y^2 = 4}

\quad \large \rm{2) \; (x - 1)^2 + (y-2)^2 = 25}

\quad \large \rm{3) \; (x - 3)^2 + (y + 6)^2 = 121}

\quad \large \rm{4) \; (x + 2)^2 + (y+7)^2 = 225}

\quad \large \rm{5) \; (x + 5)^2 + (y-8)^2 = 18}

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\largenderline{\mathbb{SOLUTION}:}

» The equation of the circle can be written in standard form as:

  • (x - h)^2 + (y - k)^2 = r^2

» Where (h, k) is the center and r is the radius.

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#1: Center = (0, 0) and Radius = 2

  • (x - 0)^2 + (y-0)^2 = 2^2

  • x^2 + y^2 = 4

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#2: Center = (1, 2) and Radius = 5

  • (x - 1)^2 + (y-2)^2 = 5^2

  • (x - 1)^2 + (y-2)^2 = 25

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#3: Center = (3, -6) and Radius = 11

  • (x - 3)^2 + (y-(\text-6))^2 = 11^2

  • (x - 3)^2 + (y + 6)^2 = 121

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#4: Center = (-2, -7) and Radius = 15

  • (x -(\text-2))^2 + (y-(\text-7))^2 = 15^2

  • (x + 2)^2 + (y+7)^2 = 225

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#5: Center = (-5, 8) and Radius = 3√2

  • (x - (\text-5))^2 + (y-8)^2 = (3\sqrt2\,)^2

  • (x + 5)^2 + (y-8)^2 = 9(2)

  • (x + 5)^2 + (y-8)^2 = 18

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(ノ^_^)ノ


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