Question

Find the centre and radius of the following:

x² + y² − 6x − 8y − 24 = 0

Answer 1

Given equation of the circle is

x² + y² − 6x − 8y − 24 = 0

Comparing this equation with

x² + y² + 2gx + 2fy + c = 0, we get

2g = − 6, 2f = − 8 and c = − 24

∴ g = − 3, f = − 4 and c = − 24

∴ Centre of the circle = (−g, −f) = (3, 4)

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

= ${\displaystyle \sqrt{{(-3)}^2+{(-4)}^2-(-24)}}$

= ${\displaystyle \sqrt{9+16+24}}$

= ${\displaystyle \sqrt{49}}$

= 7.