WAEC Further Mathematics 2023 Paper

Standard Form equation of a circle (Center-Radius Form): $(x - a)^2 + (y - b)^2 = r^2$

$2x^2+2y^2-4x+5y+1=0$

Divide through by 2

= $x^2+y^2-2x+\frac{5}{2}y+\frac{1}{2}=0$

=$x^2-2x+y^2+\frac{5}{2}y=-\frac{1}{2}$

=$x^2-2x+1^2+y^2+\frac{5}{2}y+\left(\frac{5}{4}\right)^2-1-\frac{25}{16}=-\frac{1}{2}$

=$(x-1)^2+\left(y+\frac{5}{4}\right)^2=-\frac{1}{2}+1+\frac{25}{16}$

=$(x-1)^2+\left(y-\left(-\frac{5}{4}\right)\right)^2=\frac{33}{16}$

=$(x-1)^2+\left(y-\left(-\frac{5}{4}\right)\right)^2=\left(\frac{\sqrt[3]{3}}{4}\right)^2$

$\therefore a = 1, b = -\frac{5}{4} \text{ and}$ $r \frac{\sqrt[3]{3}}{4} \text{ (answer)}$