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24 October, 01:17

What is the radius of the circle x^2+y^2+21=10x

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  1. 24 October, 01:23
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    The radius of the given equation is 2.

    Step-by-step explanation:

    The equation of a circle whose center (h, k) and radius is r,

    (x - h) ² + (y - k) ² = r² ... (i)

    Here given that-

    x² + y² + 21 = 10 x

    x² - 10 x + y² + 21 = 0

    (To making perfect square, add and subtract 25) -

    x² - 10 x + 25 - 25 + y² + 21 = 0

    (x² - 10 x + 25) + y² - 4 = 0

    [As we know that -

    (x - 5) ² = x² - 10 x + 25]

    (x - 5) ² + y² = 4

    (x - 5) ² + (y - 0) ² = 4

    (x - 5) ² + (y - 0) ² = 2² ... (ii)

    On comparing equation (i) and (ii) -

    r = 2

    Hence the radius of the given equation is 2 and center is (5, 0).
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