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Asa Gordon
Mathematics
24 October, 01:17
What is the radius of the circle x^2+y^2+21=10x
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Annalise Valdez
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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