Answer:
(-7, -5)
Step-by-step explanation:
x² + y² + 14x + 10y − 7 = 0
Strategy:
Convert the equation to the centre-radius form:
(x - h)² + (y - k)² = r²
The centre of the circle is at (h, k) and the radius is r
Solution:
Group x and y terms together; move the number to the right-hand side.
x² + 14x + y² + 10y = 7
Complete the square for x
(Take half the coefficient of x, square it, and add to each side of the equation)
(14/2)² = 7² = 49
(x² + 14x + 49) + (y² + 10y) = 56
Complete the square for y
(Take half the coefficient of y, square it, and add to each side of the equation)
(10/2)² = 5² =25
(x² + 14x + 49) + (y² + 10y + 25 ) = 81
Express the result as the sum of squares
(x + 7)² + (y + 5)² = 9²
h = -7; k = -5; r = 9
The centre of the circle is at (-7, -5).
The graph of the circle below has its centre at (-7, -5) and radius 9.
