Answer:
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
