Question

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

Answer 1

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

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