The equation for the circle is:

x2+y2+14x+10y-7=0.

What is the center of the circle?

Enter your answer in the boxes.

(-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.