Question

Find the centre and radius of the circle

x² + y² – 22x – 4y + 25 = 0

Answer 1

Comparing x² + y² – 22x – 4y + 25 = 0 with general equation of circle x² + y² + 2gx + 2fy + c = 0

We get 2g = -22, 2f = -4, c = 25

g = -11, f = -2, c = 25

Centre = (-g, -f) = (11, 2)

Radius = `sqrt(g^2 + f^2 - c)`

`= sqrt((- 11)^2 + (-2)^2 - 25)`

`= sqrt(121+4-25)`

`= sqrt100` = 10