Answer:
The equation of the circle <em>(x + 5 )² + ( y + 10 )² = (4)²</em>
<em>Center of the circle ( h, k) = ( -5 , -10)</em>
<em>Radius of the circle ' r' = 4</em>
Step-by-step explanation:
<u><em>Explanation</em></u>:-
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
<em>By using formula </em>
<em>(a+b)² = a² + 2 a b + b²</em>
<em>(x + 5 )² + ( y + 10 )² - 25 - 100 + 109 = 0</em>
<em>(x + 5 )² + ( y + 10 )² - 16 = 0</em>
<em>(x + 5 )² + ( y + 10 )² = 16</em>
(x + 5 )² + ( y + 10 )² = (4)²
The standard equation of the circle ( x - h )² + ( y -k)² = r²
<em> Center of the circle ( h, k) = ( -5 , -10)</em>
<em>Radius of the circle ' r' = 4</em>
<u><em>Conclusion</em></u><em>:-</em>
The equation of the circle <em>(x + 5 )² + ( y + 10 )² = (4)²</em>
<em>Center of the circle ( h, k) = ( -5 , -10)</em>
<em>Radius of the circle ' r' = 4</em>
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