Standard and General Form of the Circle's Equation?

Write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k).

(1) r = 3; (h, k) = (0, 0 )

(2) r = 5; (h, k) = (-5, 2)

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  • 1 decade ago
    Favorite Answer

    (1) r = 3; (h, k) = (0, 0 )

    General Form:

    x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0

    x^2 + y^2 + 2(0)x - 2(0)y + 0^2 + 0^2 - 3^2 = 0

    x^2 + y^2 - 3^2 = 0

    x^2 + y^2 - 9 = 0 ANS.

    Standard Form:

    (x - h)^2 + (y - k)^2 = r^2

    (x - 0)^2 + (y - 0)^2 = 3^2

    x^2 + y^2 = 9 ANS.

    2) r = 5; (h, k) = (-5, 2)

    General Form:

    x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0

    x^2 + y^2 - 2(-5)x - 2(2)y + (-5)^2 + 2^2 - 5^2 = 0

    x^2 + y^2 + 10x - 4y + 25 + 4 - 25 = 0

    x^2 + y^2 + 10x - 4y + 4 = 0 ANS

    Standard Form:

    (x - h)^2 + (y - k)^2 = r^2

    (x - -5)^2 + (y - 2)^2 = 5^2

    (x + 5)^2 + (y - 2)^2 = 25 ANS

    teddy boy

  • 4 years ago

    General Form Of A Circle

  • Anonymous
    6 years ago

    RE:

    Standard and General Form of the Circle's Equation?

    Write the standard form of the equation and the general form of the equation of each circle of radius r and center (h, k).

    (1) r = 3; (h, k) = (0, 0 )

    (2) r = 5; (h, k) = (-5, 2)

    Source(s): standard general form circle 39 equation: https://trimurl.im/j56/standard-and-general-form-o...
  • cidyah
    Lv 7
    1 decade ago

    The standard form is (x-h)^2+(y-k)^2=r^2, (h,k) is the center and r, the radius.

    1) (x-0)^2+(y-0)^2=3^2

    =x^2+y^2=9

    2)(x-(-5))^2+(y-2)^2=5^2

    (x+5)^2+(y-2)^2=25

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  • Anonymous
    1 decade ago

    With centre (0,0) it is x^2 + y^2 = r^2

    (1) x^2 + y^2 = 9

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