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

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).