Question

Find the centre and radius of the following:

x² + y² − 2x + 4y − 4 = 0

Answer 1

Comparing the equation
x² + y² − 2x + 4y − 4 = 0
with the equation
x² + y² + 2gx + 2fy + c = 0, we get,

2g= − 2, 2f = 4 and c = − 4

∴ g = − 1, f = 2 and c = − 4

∴ centre of the circle = (− g, − f) = (1, − 2)

and radius of the circle = ${\displaystyle \sqrt{{\text{g}}^2+f^2-\text{c}}}$

= ${\displaystyle \sqrt{{(-1)}^2+{\left(2\right)}^2-(-4)}}$

= ${\displaystyle \sqrt{1+4+4}}$

= 3.