WAEC 2022 · Paper 1 · Q33

The equation of a circle is given as $2x^2 + 2y^2 - x - 3y - 41 = 0$ . Find the coordinates of its centre.

Worked solution (try it first)

Divide by 2 so that $x^2$ and $y^2$ have coefficient 1: $x^2 + y^2 - \frac12 x - \frac32 y - \frac{41}{2} = 0$ .
For $x^2 + y^2 + 2gx + 2fy + c = 0$ the centre is $(-g, -f)$ .
Here $2g = -\frac12$ and $2f = -\frac32$ , so $g = -\frac14$ and $f = -\frac34$ .
So the centre is $\left(\frac14, \frac34\right)$ , option B.