Question

The general form of a circle is given as x^2+y^2+4x-10y-7=0.

What are the coordinates of the center of the circle?

What is the length of the radius of the circle?

Answer 1

• center: (-2, 5)
• radius: 6

Explanation:

We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.

(x^2 +4x) +(y^2 -10y) = 7

(x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25

(x +2)^2 +(y -5)^2 = 6^2

Compare to ...

(x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle

We see that the center is ...

(h, k) = (-2, 5)

and the radius is ...

r = 6