WAEC 2023 · Paper 1 · Q33

Find the radius of the circle $2x^2 + 2y^2 - 4x + 5y + 1 = 0$ .

Worked solution (try it first)

Divide by 2 so that $x^2$ and $y^2$ have coefficient 1: $x^2 + y^2 - 2x + \frac{5}{2}y + \frac{1}{2} = 0$ .
Compare with $x^2 + y^2 + 2gx + 2fy + c = 0$ : $g = -1$ , $f = \frac{5}{4}$ , $c = \frac{1}{2}$ .
$r^2 = g^2 + f^2 - c$ , which is $1 + \frac{25}{16} - \frac{1}{2} = \frac{33}{16}$ .
So $r = \dfrac{\sqrt{33}}{4}$ , option D.