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Papessa [141]
3 years ago
6

Determine the center and radius of the following circle equation:

Mathematics
1 answer:
UkoKoshka [18]3 years ago
3 0

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>

<em></em>

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