Answer:
Center of the circle is (-9, -7)
Radius of the circle = 5 units
Explanation:
Given question is incomplete: here is the complete question.
Certain circle can be represented by the following equation. x^2+y^2+18x+14y+105=0.
What is the center of this circle ?
What is the radius of this circle ?
Since equation of the circle has been given by the equation,
x² + y² + 18x + 14y + 105 = 0
Now we will convert this equation to the standard form of the circle.
x² + 18x + y² + 14y = -105
[x² + 2(9)x] + [y² + 2(7)x] = -105
[x² + 2(9)x + 9²] + [y² + 2(7)y + 7²] = 9² + 7² - 105
(x + 9)² + (y + 7)² = 81 + 49 - 105
(x + 9)² + (y + 7)² = 25
(x + 9)² + (y + 7)² = 5²
By comparing this equation with the standard equation of the circle → (x - h)² + (y - k)² = r²
Center of the circle is (-9, -7) and radius of the circle is 5 units.