Determine the center and radius of the following circle equation:

x2 + y2 + 10x + 20y + 109 = 0

Center:

Radius:

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problem 1 out of max

The equation of the circle (x + 5) ² + (y + 10) ² = (4) ²

Center of the circle (h, k) = (-5, - 10)

Radius of the circle ' r' = 4

Step-by-step explanation:

Explanation:-

Given circle equation is x² + y² + 10 x + 20 y + 109 = 0

x² + 10 x + y² + 20 y + 109 = 0

x² + 2 (5) (x) + (5) ² - (5) ² + y² + 2 (10) y + (10) ² - (10) ² + 109 = 0

By using formula

(a+b) ² = a² + 2 a b + b²

(x + 5) ² + (y + 10) ² - 25 - 100 + 109 = 0

(x + 5) ² + (y + 10) ² - 16 = 0

(x + 5) ² + (y + 10) ² = 16

(x + 5) ² + (y + 10) ² = (4) ²

The standard equation of the circle (x - h) ² + (y - k) ² = r²

Center of the circle (h, k) = (-5, - 10)

Radius of the circle ' r' = 4

Conclusion:-

The equation of the circle (x + 5) ² + (y + 10) ² = (4) ²

Center of the circle (h, k) = (-5, - 10)

Radius of the circle ' r' = 4