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17 February, 07:16

A circle has the equation x2+y2-8x-2y-17=0.

What is the equation of the circle in standard form?

(x-4) 2 + (y-1) 2=34

(x+4) 2 + (y-1) 2=34

(x-4) 2 + (y-1) 2=17

(x+4) 2 + (y-1) 2=17

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Answers (1)
  1. 17 February, 07:31
    0
    A

    Step-by-step explanation:

    The equation of a circle in standard form is

    (x - h) ² + (y - k) ² = r²

    where (h, k) are the coordinates of the centre and r is the radius

    Given

    x² + y² - 8x - 2y - 17 = 0

    Collect the x - terms and the y - terms together and add 17 to both sides

    x² - 8x + y² - 2y = 17

    Use the method of completing the square on both x and y terms.

    add (half the coefficient of the x / y terms) ² to both sides

    x² + 2 ( - 4) x + 16 + y² + 2 ( - 1) y + 1 = 17 + 16 + 1

    (x - 4) ² + (y - 1) ² = 34 → A
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